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Items from 1 to 20 out of 78 results

article

Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators

Aysegul Ç Alabalik, Alexandre Almeida, Stefan Samko

Mathematical Methods in the Applied Sciences > 43 > 16 > 9375 - 9386

We show that certain vanishing properties defining closed subspaces of generalized Morrey spaces are preserved under the action of various classical operators of harmonic analysis, such as maximal operators, singular‐type operators, Hardy operators, and fractional integral operators. Those vanishing subspaces were recently used to deal with the delicate problem on the description of the closure of...

article

Maximal functions for Weinstein operator

Chokri Abdelkefi

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2020 > 19 > 105-119

In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ε centered at 0 on the upper half space Rd-1× ]0,+∞[. Second, we prove weak-type L1-estimates for the uncentered maximal function associated...

article

Some results on generalized Dunkl–Lipschitz spaces

Samir Kallel

Mathematische Nachrichten > 293 > 2 > 305 - 326

In this paper we study certain relations between the Dunkl–Sobolev classes of fractional order

L_{α, k}^{p} (I R)

and the generalized Dunkl–Lipschitz classes

\land_{α, p, q}^{k} (I R)

. Next, we show a Dunkl–Hardy–Littlewood theorem for k‐temperatures and its dual. Also, we give some theorems on Dunkl convolutions of Dunkl–Lipschitz functions. Finally, we establish some results concerning the Dunkl transforms of functions...

article

Boundedness of a class of rough maximal functions

Mohammed Ali, Omar Al-mohammed

Journal of Inequalities and Applications > 2018 > 2018 > 1 > 1-12

In this work, we obtain appropriate sharp bounds for a certain class of maximal operators along surfaces of revolution with kernels in Lq(Sn−1) $L^{q}(\mathbf{S}^{n-1})$, q>1 $q > 1$. By using these bounds and using an extrapolation argument, we establish the Lp $L^{p}$ boundedness of the maximal operators when their kernels are in L(logL)α(Sn−1) $L(\log L)^{\alpha}(\mathbf{S}^{n-1})$ or in...

article

Maximal and Riesz Potential Operators on Musielak–Orlicz Spaces Over Metric Measure Spaces

Takao Ohno, Tetsu Shimomura

Integral Equations and Operator Theory > 2018 > 90 > 6 > 1-18

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator $$M_{\lambda }$$ Mλ on Musielak–Orlicz spaces $$L^{\Phi }(X)$$ LΦ(X) over bounded metric measure spaces. As an application of the boundedness of $$M_{\lambda }$$ Mλ , we establish a generalization of Sobolev’s inequality for Riesz potentials $$I_{\alpha (\cdot ),\tau }f$$ Iα(·),τf with $$f \in L^{\Phi...

article

On the boundedness of a certain class of maximal functions on product spaces and extrapolation

Mohammed Al-Dolat, Mohammed Ali, Imad Jaradat, Khaldoun Al-Zoubi

Analysis and Mathematical Physics > 2019 > 9 > 1 > 453-464

In this paper, we establish $$L^{p}$$ L p estimates for certain class of maximal functions on product domains with rough kernels in $${L^{q}}(\mathbf S ^{n-1}\times \mathbf S ^{m-1})\,(n,m\ge 2).$$ L q ( S n - 1 × S m - 1 ) ( n , m ≥ 2 ) . These estimates are used in an extrapolation argument to obtain some new improved and extended results on maximal functions.

article

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

Olli Saari, Christoph Thiele

Journal of Fourier Analysis and Applications > 2019 > 25 > 1 > 167-183

We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain $$L^{p}(\mathbb {R}^{2}) \rightarrow L^{p}(\mathbb {R}^{2})$$ L p ( R 2 ) → L p ( R 2 ) bounds for all $$1<p <\infty $$ 1 < p < ∞ . We discuss various...

article

On the regularity of maximal operators supported by submanifolds

Feng Liu, Huoxiong Wu

Journal of Mathematical Analysis and Applications > 2017 > 453 > 1 > 144-158

We prove that the maximal operators supported by submanifolds are bounded and continuous on the Triebel–Lizorkin spaces Fsp,q(Rd) and Besov spaces Bsp,q(Rd) for 0<s<1 and 1<p,q<∞. As a corollary, we also show that these operators are bounded and continuous on the fractional Sobolev spaces Ws,p(Rd) for 0≤s<1 and 1<p<∞. Our main results represent significant improvements as well...

article

The Stein–Strömberg covering theorem in metric spaces

J.M. Aldaz

Journal of Mathematical Analysis and Applications > 2017 > 449 > 2 > 1741-1753

In [8] Naor and Tao extended to the metric setting the O(dlog⁡d) bounds given by Stein and Strömberg for Lebesgue measure in Rd, deriving these bounds first from a localization result, and second, from a random Vitali lemma. Here we show that the Stein–Strömberg original argument can also be adapted to the metric setting, giving a third proof. We also weaken the hypotheses, and additionally, we sharpen...

article

Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals

Dongxiang Chen, Shanzhen Lu, Suzhen Mao

Frontiers of Mathematics in China > 2017 > 12 > 3 > 531-558

This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued...

article

Boundary behavior of generalized Poisson integrals on buildings of type $$\widetilde{A}_2$$ A ~ 2

A. M. Mantero, A. Zappa

Bollettino dell'Unione Matematica Italiana > 2017 > 10 > 4 > 681-724

Let $${\Delta }$$ Δ be an affine building of type $$\widetilde{A}_2$$ A ~ 2 and $${\Omega }$$ Ω its maximal boundary. We prove that, for every function $$f \in L^1({\Omega }),$$ f ∈ L 1 ( Ω ) , restricted convergence of the normalized generalized Poisson transform $${\mathcal {P}}_{{\chi }} f / {\mathcal {P}}_{{\chi }} 1$$ P χ f / P χ 1 ...

article

Corrigendum to “Singular integral operators along surfaces of revolution” [J. Math. Anal. Appl. 274 (2) (2002) 608–625]

Hung Viet Le

Journal of Mathematical Analysis and Applications > 2016 > 442 > 2 > 820-823

One of the key estimates in the original paper [3] does not seem to hold true, which may invalidate some results of that paper. However, there is a couple of ways to fix this mistake by adding additional hypotheses in Theorem 1 [3].

article

Endpoint bounds for quasiradial Fourier multipliers

Jongchon Kim

Annali di Matematica Pura ed Applicata ( 01923 -) > 2017 > 196 > 3 > 773-789

We consider quasiradial Fourier multipliers, i.e., multipliers of the form $$m(a(\xi ))$$ m ( a ( ξ ) ) for a class of distance functions a. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $$L^p$$ L p for a certain range of p. In addition, when m is compactly supported in $$(0,\infty )$$ ( 0 , ∞ ) , we give a similar...

article

Vector-Valued Singular Integrals with Non-smooth Kernels on Spaces of Homogeneous Type

Hung Viet Le

Complex Analysis and Operator Theory > 2017 > 11 > 1 > 57-84

In this article, we obtain weighted norm inequalities for vector-valued singular integrals with non-smooth kernels on spaces of homogeneous type. Vector-valued commutators of singular integrals and BMO functions are also studied.

article

Reverse Hölder Property for Strong Weights and General Measures

Teresa Luque, Carlos Pérez, Ezequiel Rela

The Journal of Geometric Analysis > 2017 > 27 > 1 > 162-182

We present dimension-free reverse Hölder inequalities for strong $$A^*_p$$ A p ∗ weights, $$1\le p < \infty $$ 1 ≤ p < ∞ . We also provide a proof for the full range of local integrability of $$A_1^*$$ A 1 ∗ weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no...

article

L ^p estimates of rough maximal functions along surfaces with applications

Ahmad Al-Salman, Abdulla M. Jarrah

Acta Mathematica Sinica, English Series > 2016 > 32 > 8 > 925-942

In this paper, we study the L ^p mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the L ^p boundedness of various maximal oscillatory singular integrals provided that their...

article

Wiener Criteria for Existence of Large Solutions of Quasilinear Elliptic Equations with Absorption

Quoc-Hung Nguyen, Laurent Véron

Potential Analysis > 2015 > 42 > 3 > 681-697

We obtain sufficient conditions, expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities, for the existence of large solutions to equations (1) −Δ _p u + e ^u − 1 = 0 or (2) −Δ _p u + u ^q = 0 in a bounded domain Ω when q >...

article

On Hermite pseudo-multipliers

Sayan Bagchi, Sundaram Thangavelu

Journal of Functional Analysis > 2015 > 268 > 1 > 140-170

In this article we deal with a variation of a theorem of Mauceri concerning the Lp boundedness of operators M which are known to be bounded on L2. We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.

article

Quasilinear Lane–Emden equations with absorption and measure data

Marie-Françoise Bidaut-Véron, Nguyen Quoc Hung, Laurent Véron

Journal de mathematiques pures et appliquees > 2014 > 102 > 2 > 315-337

We study the existence of solutions to the equation −Δpu+g(x,u)=μ when g(x,.) is a nondecreasing function and μ a measure. We characterize the good measures, i.e. the ones for which the problem has a renormalized solution. We study particularly the cases where g(x,u)=|x|−β|u|q−1u and g(x,u)=sgn(u)(eτ|u|λ−1). The results state that a measure is good if it is absolutely continuous with respect to an...

article

Convergence properties of modular eigenfunctions for the p(⋅)-Laplacian

Jan Lang, Osvaldo Méndez

Nonlinear Analysis > 2014 > 104 > Complete > 156-170

The variation of the first Dirichlet eigenfunction for the modular p(⋅)-Laplacian is studied as a generalization of the constant case. The stability of the eigenfunctions under perturbations of the norm of the underlying spaces (i.e., with respect to perturbations of the exponent p(⋅)) is observed.

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MAXIMAL FUNCTIONS (78)
SINGULAR INTEGRALS (10)
RIESZ POTENTIALS (6)
BESOV SPACES (5)
ROUGH KERNELS (5)
42B25 (4)
COMMUTATORS (4)
FRACTIONAL INTEGRALS (4)
HARDY SPACES (4)
VARIABLE EXPONENT (4)
DUAL FEASIBLE FUNCTIONS (3)
INTERPOLATION (3)
MODULAR INEQUALITIES (3)
SOBOLEV SPACES (3)
SOBOLEV’S INEQUALITY (3)
WEIGHTS (3)
42B20 (2)
46E30 (2)
BESSEL CAPACITIES (2)
DIMENSION FREE ESTIMATES (2)
EXTRAPOLATION (2)
EXTREMAL FUNCTIONS (2)
GENERALIZED HARDY SPACES (2)
MARCINKIEWICZ INTEGRALS (2)
METRIC MEASURE SPACE (2)
MORREY SPACES (2)
MUCKENHOUPT WEIGHTS (2)
MUSIELAK–ORLICZ SPACES (2)
ORLICZ SPACES (2)
OSCILLATORY SINGULAR INTEGRALS (2)
POISSON KERNEL (2)
QUASILINEAR ELLIPTIC EQUATIONS (2)
SOBOLEV EMBEDDINGS (2)
SOBOLEV'S INEQUALITY (2)
SPACE OF HOMOGENEOUS TYPE (2)
SPACES OF HOMOGENEOUS TYPE (2)
SURFACES OF REVOLUTION (2)
TRIEBEL-LIZORKIN SPACES (2)
WAVELETS (2)
WEIGHTED INEQUALITIES (2)
WEIGHTED INEQUALTIES (2)
WOLFF POTENTIAL (2)
[MATHEMATICAL SUBJECT CODES] 42B25 (2)
L P BOUNDEDNESS (1)
$$L^P$$ L P BOUNDEDNESS (1)
$B {P,Q}^{S,\TAU }$ SPACES (1)
26A16 (1)
42A38 (1)
42B15 (1)
47B06 (1)
47B07 (1)
A.E. CONVERGENCE (1)
AHLFORS REGULARITY (1)
ALMOST DIAGONAL CONDITION (1)
ALMOST EVERYWHERE CONVERGENCE (1)
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ATOMIC DECOMPOSITION (1)
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BEST CONSTANT APPROXIMANT (1)
BLOCK SPACES (1)
BMO (1)
BMO FUNCTIONS (1)
BOREL MEASURES (1)
BOUNDARY CONDITION (1)
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BUILDINGS (1)
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DISTRIBUTION FUNCTIONI (1)
DUNKL OPERATOR (1)
DUNKL TRANSFORM (1)
EIGENVALUE PROBLEMS (1)
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EMBEDDINGS (1)
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EXTRAPOLATION OF WEIGHTED NORM INEQUALITIES (1)
FOURIER RESTRICTION AND BOCHNER–RIESZ (1)
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FREE SCHRÖDINGER EQUATION (1)
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GENERALIZED MORREY SPACES (1)
GENERALIZED SMOOTHNESS (1)
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Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators

Maximal functions for Weinstein operator

Some results on generalized Dunkl–Lipschitz spaces

Boundedness of a class of rough maximal functions

Maximal and Riesz Potential Operators on Musielak–Orlicz Spaces Over Metric Measure Spaces

On the boundedness of a certain class of maximal functions on product spaces and extrapolation

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

On the regularity of maximal operators supported by submanifolds

The Stein–Strömberg covering theorem in metric spaces

Multiple weighted estimates for maximal vector-valued commutator of multilinear Calderón-Zygmund singular integrals

Boundary behavior of generalized Poisson integrals on buildings of type $$\widetilde{A}_2$$ A ~ 2

Corrigendum to “Singular integral operators along surfaces of revolution” [J. Math. Anal. Appl. 274 (2) (2002) 608–625]

Endpoint bounds for quasiradial Fourier multipliers

Vector-Valued Singular Integrals with Non-smooth Kernels on Spaces of Homogeneous Type

Reverse Hölder Property for Strong Weights and General Measures

L ^p estimates of rough maximal functions along surfaces with applications

Wiener Criteria for Existence of Large Solutions of Quasilinear Elliptic Equations with Absorption

On Hermite pseudo-multipliers

Quasilinear Lane–Emden equations with absorption and measure data

Convergence properties of modular eigenfunctions for the p(⋅)-Laplacian

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