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In this paper we pursue the study of the best approximation operator extended from LΦ to Lφ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calderón–Zygmund class tmp (x) which had been introduced in 1961. We also obtain weak and strong type inequalities...
In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space \(W^1L^\Phi([0,T])\). We employ the direct method of calculus of variations and we consider a potential function \(F\) satisfying the inequality \(|\nabla F(t,x)|\leq b_1(t) \Phi_0'(|x|)+b_2(t)\), with \(b_1, b_2\in L^1\) and certain \(N\)-functions \(\Phi_0\).
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