Approximation by integral functions of finite degree in variable exponent Lebesgue spaces on the real axis

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

Approximation of hypersingular integral transforms on the real axis

where wα,β(x) = |x|αe−|x| β is a generalized Freud weight with α ≥ 0, β > 1 and 0 ≤ p ∈ N. This topic is of interest, for instance, in the numerical solution of hypersingular integral equations, which are often models for physics and engineering problems (see [5, 2, 4]). To our knowledge, most of the papers available in the literature deal with the approximation of Hadamard integrals on bounded...

On Variable Exponent Amalgam Spaces

We derive some of the basic properties of weighted variable exponent Lebesgue spaces L p(.) w (R) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W (L p(.) w , L q υ) is defined, where the local component is a weighted variable exponent Lebesgue space L p(.) w (R) and the global component is a weighted Lebesgue space Lυ (R) . We inves...

The Sampling Theorem in Variable Lebesgue Spaces

hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...

Interpolation in Variable Exponent Spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.