Interpolation theorems for variable exponent Lebesgue spaces

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

Interpolation orbits in the Lebesgue spaces

This paper is devoted to description of interpolation orbits with respect to linear operators mapping an arbitrary couple of L p spaces with weights {L p 0 (U 0), L p 1 (U 1)} into an arbitrary couple {L q 0 (V 0), L q 1 (V 1)}, where 1 ≤ p 0 , p 1 , q 0 , q 1 ≤ ∞. By L p (U) we denote the space of measurable functions f on a measure space M such that f U ∈ L p with the norm f Lp(U) = f U Lp. }...

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.

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...