Related papers: Lorentz spaces with variable exponents

Multilinear $L^p$ extrapolation results are established in a limited-range, multilinear, and off-diagonal setting for mixed-norm Lebesgue spaces over $\sigma$-finite measure spaces. Integrability exponents are allowed in the full range…

We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between Grand Lebesgue and classical Lebesgue-Riesz spaces and we…

We investigate the properties of the variable Lebesgue spaces with quasi-norm on a probability space, and give the atomic decompositions suited to the variable exponent martingale Hardy spaces. Using the decompositions and the harmonic mean…

We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.

In this note, we establish several interpolation inequalities in $\mathbb R^n$ in the Lebesgue spaces and Morrey spaces. By using the classical Calderon--Zygmund decomposition, we will reprove that $L^{p}(\mathbb…

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…

We study the classical spaces $L_{p}$ and $\ell_{p}$ for the whole range $0<p<\infty$ from a metric viewpoint and give a complete Lipschitz embeddability roadmap between any two of those spaces when equipped with both their ad-hoc distances…

We prove that the $Z$-spaces $Z^{p,q}_s$ form a complex interpolation scale for all $0 < p,q \leq \infty$ and $s \in \mathbb{R}$, filling a gap in recent work with Pascal Auscher.

We extend to n-dimensions a characterization of the Marcinkiewicz $L(p,\infty)$ spaces first obtained by Garsia-Rodemich in the one dimensional case. This leads to a new proof of the John-Nirenberg self-improving inequalities. We also show…

In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…

Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…

Given $E_0, E_1, E, F$ rearrangement invariant spaces, $a, b, b_0, b_1$ slowly varying functions and $0\leq \theta_0<\theta_1\leq 1$, we characterize the interpolation space $$(\overline{X}_{\theta_0,b_0,E_0}, \overline{X}^{\mathcal…

We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) embeds completely isomorphically into a noncommutative $L_p$-space, where $C_p$ and $R_p$ are respectively the $p$-column and $p$-row Hilbertian operator spaces. We also…

We characterize the compactness of embedding derivatives from Hardy space $H^p$ into Lebesgue space $L^q(\mu)$. We also completely characterize the boundedness and compactness of derivative area operators from $H^p$ into…

In this paper, we prove a new continuous embedding theorem for fractional Sobolev spaces with variable exponents into variable exponent Lebesgue spaces on unbounded domains. As an application, we study a class of nonlocal elliptic problems…

We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(\alpha,p,q)(X)$ on domains which support a Markovian kernel with appropriate exponential bounds. This extends former results of \cite{Jon,KPP1,KPP2,GHL} which were…

We use the compactness theorem of continuous logic to give a new proof that $L^r([0,1]; \mathbb{R})$ isometrically embeds into $L^p([0,1]; \mathbb{R})$ whenever $1 \leq p \leq r \leq 2$. We will also give a proof for the complex case. This…

In the sequel, we recall and comment some classical results on the non-increasing rearrangement and Lorentz spaces. There are papers in the existing literature that seemed to have been bypassed as regards its contractive property in~$L^p$…

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for $p\in [1,\infty]$, every proper subset of $L_p$ is almost Lipschitzly embeddable into a Banach space $X$ if and only if $X$…

The sequence of entropy numbers quantifies the degree of compactness of a linear operator acting between quasi-Banach spaces. We determine the asymptotic behavior of entropy numbers in the case of natural embeddings between…