Lipschitz type smoothness of the fractional integral on variable exponent spaces

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...

Poincaré-type Inequality for Variable Exponent Spaces of Differential Forms

We prove both local and global Poincaré inequalities with the variable exponent for differential forms in the John domains and s L -averaging domains, which can be considered as generalizations of the existing versions of Poincaré inequalities.

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.

Function Spaces of Variable Smoothness and Integrability

A. In this article we introduce Triebel–Lizorkin spaces with variable smoothness and integrability. Our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years. Vector-valued maximal inequalities do not work in the generality which we pursue, and an alternate approach is thus developed. Applying it, we give molecular ...

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