The field of variable exponent function spaces has witnessed an explosive growth in recent
years. The standard reference article for basic properties is already 20 years old. Thus this …

This book is a result of our ten-year fruitful collaboration. It deals with integral operators of
harmonic analysis and their various applications in new, non-standard function spaces …

We study the boundedness of the maximal operator on the weighted variable exponent
Lebesgue spaces L ω p (·)(Ω). For a given log-Hölder continuous exponent p with 1< inf p⩽ …

In this article a new method for moving from local to global results in variable exponent
function spaces is presented. Several applications of the method are also given: Sobolev …

In this article we define an appropriate Muckenhoupt class for variable exponent Lebesgue
spaces, in other words, we characterize the set of weights ω for which the maximal operator …

We study the Hardy type, two-weight inequality for the multidimensional Hardy operator in
the variable exponent Lebesgue space L p (.)(ℝ n). We prove equivalent conditions for L p …

A Hardy type two-weighted inequality is investigated for the multidimensional Hardy
operator in the norms of generalized Lebesgue spaces L p (·). Equivalent necessary and …

The boundedness of Hardy type operator [Formula: see text] is studied in weighted variable
exponent Lebesgue spaces Lp (⋅). The necessary and sufficient criterion established on the …

We prove that in variable exponent spaces $ L^{p (\cdot)}(\Omega) $, where $ p (\cdot) $
satisfies the log-condition and $\Omega $ is a bounded domain in $\mathbf R^ n $ with the …

We give a new proof for power-type weighted Hardy inequality in the norms of generalized
Lebesgue spaces. Assuming the logarithmic conditions of regularity in a neighborhood of …