相关论文: The sharp $A_p$ constant for weights in a reverse-…

In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context.…

In this paper, we will obtain the sharp constant for multilinear integral operator on Heisenberg group Lebesgue space which is based on the Stein-Weiss lemma, the boundedness for multilinear integral operator on Heisenberg group $A_p$…

We give sharp remainder terms of $L^{p}$ and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised…

We give a weak-type counterpart of the main result in an earlier work of the first author, E. Rela and T. Luque which allows to provide a lower bound for the exponent of the $A_{p}$ constant in terms of the behaviour of the unweighted…

In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John--Nirenberg inequality and $L^p$ estimations of BMO functions. In the present…

We precisely characterize the relationships between the reverse H\"older inequality, the Fujii-Wilson condition, the B\'ekoll\'e-Bonami $\mathrm{B}_p$ condition, the $\mathrm{B}_\infty$ condition, and the reverse Jensen inequality, for…

We study the regularity of the $p$-Poisson equation $$ \Delta_p u = h, \quad h\in L^q $$ in the plane. In the case $p>2$ and $2<q<\infty$ we obtain the sharp H\"older exponent for the gradient. In the other cases we come arbitrarily close…

In this paper we revisit the remainder terms of $L^p$-Hardy inequalities for magnetic $p$-Laplacians. In particular, we will give an integral representation of the sharp constant for a crucial algebraic inequality established by C. Cazacu,…

The paper is devoted to two-weight estimates for the fractional maximal operators $\mathcal{M}^\alpha$ on general probability spaces equipped with a tree-like structure. For given $1<p\leq q<\infty$, we study the sharp universal upper bound…

In this paper we prove self-improvement properties of strong Muckenhoupt and Reverse H\"older weights with respect to a general Radon measure on $\mathbb{R}^n$. We derive our result via a Bellman function argument. An important feature of…

To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…

We prove a sharp quantitative version of the $p$-Sobolev inequality for any $1<p<n$, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for $p<2$, while it…

Given $1\leq q<p<\infty$ quantitative weighted L^p estimates, in terms of Aq weights, for vector valued maximal functions, Calder\'on-Zygmund operators, commutators and maximal rough singular integrals are obtained. The results for singular…

This paper is a continuation of earlier work by the first author who determined the John--Nirenberg constant of ${\rm BMO}^p\big((0,1)\big)$ for the range $1\le p\le 2.$ Here, we compute that constant for $p>2.$ As before, the main results…

This is the first in our series of papers concerning some Hardy-Littlewood-Sobolev type inequalities. In the present paper, the main objective is to establish the following sharp reversed HLS inequality in the whole space $\mathbb R^n$…

Extending results in \cite{M} and \cite{MM} we characterize the classical classes of weights that satisfy reverse H\"{o}lder inequalities in terms of indices of suitable families of $K-$functionals of the weights. In particular, we…

An equivalent norm in the weighted Bergman space $A^p_\omega$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also…

We study sharp weighted Sobolev-type inequalities of the form \[ \int_{0}^{1}|u(x)|\rho(x) \diff x \leqslant \Lambda \Bigl(\int_{0}^{1}|u^{(k)}(x)|^2 \diff x\Bigr)^{1/2}, \qquad u\in H_0^k(0,1), \] where $\rho$ is a non-negative weight. We…

In this paper, we study both elliptic and parabolic equations in non-divergence form with singular degenerate coefficients. Weighted and mixed-norm $L_p$-estimates and solvability are established under some suitable partially weighted BMO…

In this paper, we will study a class of linear integral operators with the nonnegative kernels on higher-dimensional product spaces, the norms of the operators can be obtained by integral of the product of the kernel function and finitely…