Sobolev's inequality for Riesz potentials in Lorentz spaces of variable exponent

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces ∗

We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L to variable exponent weak Lebesgue spaces.

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.

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...

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