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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

Quantitative uncertainty principles for the Weinstein transform

A. Abouelaz, A. Achak, R. Daher, N. Safouane

Boletín de la Sociedad Matemática Mexicana > 2019 > 25 > 2 > 375-383

The Weinstein transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. Donoho–Stark’s uncertainty principle is obtained for the Weinstein transform.

article

Benedicks–Amrein–Berthier type theorem related to Weinstein transform

A. Achak, R. Daher

Analysis Mathematica > 2017 > 43 > 4 > 511-521

The aim of this paper is to prove a new uncertainty principle for the Weinstein transform. This result is an extension of a result of Benedicks, Amrein and Berthier, which states that a nonzero function f and its Weinstein transform F_α(f) cannot both have support of finite measure. We also extend Donoho–Strak’s local uncertainty principle to the Weinstein transform.

article

Weinstein-Sobolev spaces of exponential type and applications

Hassen Ben Mohamed, Belgacem Ghribi

Acta Mathematica Sinica, English Series > 2013 > 29 > 3 > 591-608

In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.

article

Uncertainty principles for the weinstein transform

Hatem Mejjaoli, Makren Salhi

Czechoslovak Mathematical Journal > 2011 > 61 > 4 > 941-974

The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi’s theorem, Beurling’s theorem, and Donoho-Stark’s uncertainty principle are obtained for the Weinstein transform.

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Keywords

WEINSTEIN TRANSFORM (5)
DONOHO–STARK’S UNCERTAINTY PRINCIPLE (2)
WEINSTEIN OPERATOR (2)
BENEDICKS–AMREIN–BERTHIER’S THEOREM (1)
BEURLING’S THEOREM (1)
COWLING-PRICE’S THEOREM (1)
DISTRIBUTION (1)
DONOHO-STARK’S UNCERTAINTY PRINCIPLE (1)
HARDY’S TYPE THEOREM (1)
MAXIMAL FUNCTIONS (1)
MIYACHI’S THEOREM (1)
SOBOLEV SPACES (1)
WEINSTEIN TRANSLATION OPERATORS (1)
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Search results

Maximal functions for Weinstein operator

Quantitative uncertainty principles for the Weinstein transform

Benedicks–Amrein–Berthier type theorem related to Weinstein transform

Weinstein-Sobolev spaces of exponential type and applications

Uncertainty principles for the weinstein transform

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