未找到相关数据
HYPERSINGULAR INTEGRALS IN POWER-WEIGHTED VARIABLE GENERALIZED HÖLDER SPACES OVER METRIC MEASURE SPACES“Hypersingular integrals in Hω(·)(Ω,w)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{\,\omega (\cdot )} (\Omega , w)$$\end{document} with power w ”
被引：0
作者：
Yuri E. Drobotov
[1
]
Boris G. Vakulov
[2
]
机构：
[1] Southern Federal University,
[2] North-Caucasus Center for Mathematical Research of the Vladikavkaz Scientific Centre of the Russian Academy of Sciences,undefined
[3] Don State Technical University,undefined
关键词：
Boundedness theorem;
Continuity;
Variable generalized Hölder spaces;
Hypersingular integral;
Integral equations;
Local modulus of continuity;
Modulus of submetry;
Zygmund type estimates;
D O I：
10.1007/s10958-024-07162-5
中图分类号：
学科分类号：
摘要：
The weighted variable generalized Hölder spaces Hω(·)(Ω,w)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$H^{\,\omega (\cdot )} (\Omega , w)$$\end{document} defined in terms of the local modulus of continuity are considered. Zygmund-type estimates are obtained for a hypersingular integral operator Dα\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$D^\alpha$$\end{document} defined on a bounded open set Ω\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\Omega$$\end{document} of a metric measure space X=(X,d,μ)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {X} = (\mathcal {X}, d, \mu )$$\end{document}, assuming the power weight function w(x)=dν(x,a)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$w(x) = d^{\,\nu }(x, a)$$\end{document}, where a,x∈Ω\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$a, x \in \Omega$$\end{document}, 1<Reν<N+1\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$1< \textrm{Re}\,\nu < N + 1$$\end{document}, and N is a parameter that characterizes the measure of balls in X\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathcal {X}$$\end{document} with respect to their radius. Based on these estimates, it is proven that, under specific conditions on the characteristic ω(x,h)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\omega (x, h)$$\end{document} of Hω(·)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$H^{\,\omega (\cdot )}$$\end{document}, Dα\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$D^\alpha$$\end{document} is a bounded operator from Hω(·)(Ω,w)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$H^{\,\omega (\cdot )} (\Omega , w)$$\end{document} to Hω-α(·)(Ω,w)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$H^{\,\omega _{-\alpha } (\cdot )} (\Omega , w)$$\end{document}, where ω-α(x,h):=h-Reαω(x,h)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\omega _{-\alpha } (x, h):= h^{\,-\textrm{Re}\,\alpha } \, \omega (x, h)$$\end{document}. This result complements a similar one for the case of 0<Reν≤1\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$0 < \textrm{Re}\,\nu \le 1$$\end{document} that was obtained in a previous study conducted by the authors.
引用
收藏
页码：168 / 187
页数：19
相关论文