Bochkariev's theorem states that for any uniformly bounded orthonormal system Φ, there is a Lebesgue integrable function such the Fourier series of it with respect to Φ diverges on set positive measure. In this paper, we extended some class variable exponent spaces. We characterized spaces Lp(⋅)[0;1], 1<p(x)<∞ a.e. [0;1], above mentioned Bochkarev's valid.

In this paper, we analyze multi-dimensional quasi-asymptotically $c$-almost periodic functions and their Stepanov generalizations as well Weyl type functions. We also several important subclasses of the class reconsider notion semi-$c$-periodicity in setting, working general framework Lebesgue spaces with variable exponent. provide certain applications our results to abstract Volterra integro-d...

Abstract In this paper, we consider the maximal operator related to Laplace-Bessel differential ( B B -maximal operator) on L p ( ⋅ ) , γ R</m:mi...

double system of exponents with complex-valued coefficients is considered. under some conditions on the coefficients, we prove that if this system forms a basis for the morrey-lebesgue type space on $left[-pi , pi right]$, then it is isomorphic to the classical system of exponents in this space.

The universality of neural networks with sigmoidal or discriminatory functions are characterized on functional Banach lattices. This study is an extension a previous similar problem unbounded exponent in variable Lebesgue spaces, which contain essentially bounded measurable functions. However, the notion lattices includes other fundamental function spaces and our result natural generalization w...