Let A be a general expansive matrix and let X ball quasi-Banach function space on $${\mathbb {R}}^n$$ , whose certain power (namely its convexification) supports Fefferman–Stein vector-valued maximal inequality the associate of other boundedness powered Hardy–Littlewood operator. The authors first introduce some anisotropic Campanato-type spaces associated with both X, prove that these are dual...

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

We consider the monomial weight |x1|1 · · · |xn|n in R, where Ai ≥ 0 is a real number for each i = 1, ..., n, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of the classical ones with the Lebesgue measure dx replaced by |x1|1 · · · |xn|ndx, and they contain the best or critical exponent (which depends on A1, ..., An). More i...

Abstract In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak spaces. The primary aim study is to a necessary sufficient condition operator induced by diffeomorphism particular, detailed information derived from boundedness, i.e., bi-Lipschitz continuity mapping that induces follows mapping. idea proof determine norm characteristic functions, e...

The current paper establishes the sharp weak bounds of p-adic fractional Hardy operator. Furthermore, optimal type estimates for operator on central Morrey space are also acquired.

The main goal of this article is to provide estimates mild solutions Navier–Stokes equations with arbitrary external forces in Rn for n≥2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known and Herz considered works equations. Morrey–Sobolev based weak-Herz space denoted as WK˙p,qαMμs WK˙p,qαN˙μ,rs, respectively, represent new properties interpolations. This class...

In this paper we have shown that associated and dual spaces of local Morrey-type spaces are ”so called” complementary local Morrey-type spaces. Our method is based on characterization of multidimensional reverse Hardy inequalities.

Let X be a ball quasi-Banach function space on Rn satisfying some mild assumptions and let α∈(0,n) β∈(1,∞). In this article, when α∈(0,1), the authors first find reasonable version I˜α of fractional integral Iα Campanato-type LX,q,s,d(Rn) with q∈[1,∞), s∈Z+n, d∈(0,∞). Then prove that is bounded from LXβ,q,s,d(Rn) to if only there exists positive constant C such that, for any B⊂Rn,|B|αn≤C‖1B‖Xβ−...

We study a natural question that, apparently, has not been well addressed in the literature. Given functions u with support unit ball B 1 ? R n and gradient Morrey space M p , ? ( ) where < what is largest range of exponents q for which necessarily ? L ? While David R. Adams proved 1975 that this embedding holds ? / ? an article from 2011 claimed larger . Here we disprove last statement by cons...