Related papers: Multilinear H\"older-type inequalities on Lorentz …
The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming $\ell_p$-sums of Banach spaces, and obtain…
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and K\"ahler manifolds.
We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities.
We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…
This work explores the interaction between different norms in infinite-dimensional vector spaces, focusing on their impact on Banach space structures and topological properties. We examine norms induced by bijective linear maps, the…
In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\cite{Sa}, \cite{CaSoA}). However, the question for multidimensional Lorentz spaces is still open. In this paper,…
We characterise $L_p$-norms on the space of integrable step functions, defined on a probabilistic space, via H\"older's type inequality with an optimality condition.
The aim of this paper is to present necessary and sufficient conditions for generalized H\"{o}lder's inequality on generalized Morrey spaces. We also obtain similar results on weak Morrey spaces and on generalized weak Morrey spaces. The…
Several new trace norm inequalities are established for 2n x 2n block matrices, in the special case where the four n x n blocks are diagonal. Some of the inequalities are non-commutative analogs of Hanner's inequality, others describe the…
Based on the local fractional calculus, we establish some new generalizations of H\"{o}lder's inequality. By using it, some results on the generalized integral inequality in fractal space are investigated in detail.
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present…
We give a generalization of a theorem of B\^ocher for the Laplace equation to a class of conformally invariant fully nonlinear degenerate elliptic equations. We also prove a Harnack inequality for locally Lipschitz viscosity solutions and a…
This paper deals with two separate but related results. First we consider weak solutions to a parabolic operator with H\"ormander vector fields. Adapting the iteration scheme of J\"urgen Moser for elliptic and parabolic equations in…
This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…
The notions of higher-order weighted multilinear Poincar\'e and Sobolev inequalities in Carnot groups are introduced. As an application, weighted Leibnitz-type rules in Campanato-Morrey spaces are established.
We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…
In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error…
Classical interpolation inequality of the type $\|u\|_{X}\leq C\|u\|_{Y}^{\theta}\|u\|_{Z}^{1-\theta}$ is well known in the case when $X$, $Y$, $Z$ are Lebesgue spaces. In this paper we show that this result may be extended by replacing…
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.