scholarly journals Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball

2021 ◽  
Vol 46 (2) ◽  
pp. 1031-1052
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Unit Ball ◽  
Morrey Spaces ◽  
Sobolev Inequalities ◽  
Sobolev Functions

scholarly journals Sharp Exponential Integrability for Traces of Monotone Sobolev Functions

2008 ◽  
Vol 192 ◽  
pp. 137-149 ◽  
Author(s):  
Pekka Pankka ◽  
Pietro Poggi-Corradini ◽  
Kai Rajala
Keyword(s):  
Unit Ball ◽  
Exponential Integrability ◽  
Geometric Methods ◽  
Sobolev Functions ◽  
Integrability Of Functions ◽  
Monotone Sobolev Functions

AbstractWe answer a question posed in [12] on exponential integrability of functions of restricted n-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.

scholarly journals Boundary growth of Sobolev functions of monotone type for double phase functionals

2021 ◽  
Vol 47 (1) ◽  
pp. 23-37
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Unit Ball ◽  
Bounded Function ◽  
Spherical Means ◽  
Hölder Continuous ◽  
Double Phase ◽  
Sobolev Functions ◽  
Monotone Type

Our aim in this paper is to deal with boundary growth of spherical means of Sobolev functions of monotone type for the double phase functional \(\Phi_{p,q}(x,t) = t^{p} + (b(x) t)^{q}\) in the unit ball B of \(\mathbb{R}^n\), where \(1 < p < q < \infty\) and \(b(\cdot)\) is a non-negative bounded function on B which is Hölder continuous of order \(\theta \in (0,1]\).

scholarly journals Hardy-Littlewood-Sobolev Inequalities onp-Adic Central Morrey Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qing Yan Wu ◽  
Zun Wei Fu
Keyword(s):  
Riesz Potential ◽  
Morrey Spaces ◽  
Sobolev Inequalities

We establish the Hardy-Littlewood-Sobolev inequalities onp-adic central Morrey spaces. Furthermore, we obtain theλ-central BMO estimates for commutators ofp-adic Riesz potential onp-adic central Morrey spaces.

HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS

2019 ◽  
pp. 1-34 ◽  
Author(s):  
YOSHIHIRO MIZUTA ◽  
TAKAO OHNO ◽  
TETSU SHIMOMURA
Keyword(s):  
Unit Ball ◽  
Variable Exponent ◽  
Type Inequality ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Hölder Continuous ◽  
Double Phase ◽  
Sobolev Type Inequality

Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent$p_{1}(\cdot )$approaching$1$and for double phase functionals$\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$, where$a(x)^{1/p_{2}}$is nonnegative, bounded and Hölder continuous of order$\unicode[STIX]{x1D703}\in (0,1]$and$1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$. We also establish Sobolev type inequality for Riesz potentials on the unit ball.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

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