Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...
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Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild *** HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by *** this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy *** results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey ***,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on R-n and X a ball quasi-Banach function space on R-n satisfying some mild assumptions. Denote by H-X...
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Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on R-n and X a ball quasi-Banach function space on R-n satisfying some mild assumptions. Denote by H-X,(L) (R-n) the Hardy space, associated with both L and X, which is defined via the Lusin area function related to the semigroup generated by L. In this article, the authors establish both the maximal function and the Riesz transform characterizations of H-X,H- L (R-n). The results obtained in this article have a wide range of generality and can be applied to the weighted Hardy space, the variableHardy space, themixed-normHardy space, theOrlicz-Hardy space, the Orlicz-slice Hardy space, and the Morrey-Hardy space, associated with L. In particular, even when L is a second order divergence form elliptic operator, both the maximal function and the Riesz transform characterizations of the mixed-norm Hardy space, the Orlicz-slice Hardy space, and the Morrey-Hardy space, associated with L, obtained in this article, are completely new.
We give necessary and sufficient conditions for the boundedness of the maximal commutators Mb$$ {M}_b $$ and the commutators of the maximal operator [b,M]$$ \left[b,M\right] $$ in total Morrey spaces Lp,lambda,mu(Doub...
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We give necessary and sufficient conditions for the boundedness of the maximal commutators Mb$$ {M}_b $$ and the commutators of the maximal operator [b,M]$$ \left[b,M\right] $$ in total Morrey spaces Lp,lambda,mu(Double-struck capital Rn)$$ {L}<^>{p,\lambda, \mu}\left({\mathrm{\mathbb{R}}}<^>n\right) $$ when b$$ b $$ belongs to Lipschitz spaces Lambda beta(Double-struck capital Rn)$$ {\dot{\Lambda}}_{\beta}\left({\mathrm{\mathbb{R}}}<^>n\right) $$, whereby some new characterizations for certain subclasses of Lipschitz spaces Lambda beta(Double-struck capital Rn)$$ {\dot{\Lambda}}_{\beta}\left({\mathrm{\mathbb{R}}}<^>n\right) $$ are obtained.
The aim of this paper is to study the maximal commutators Mb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} ...
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The aim of this paper is to study the maximal commutators Mb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{b}$$\end{document} and the commutators of the maximal operator [b, M] in the total Morrey spaces Lp,lambda,mu(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>{p,\lambda ,\mu }(\mathbb {G})$$\end{document} on any stratified Lie group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {G}$$\end{document} when b belongs to Lipschitz spaces Lambda(center dot)beta(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\Lambda }}_{\beta }(\mathbb {G})$$\end{document}. Some new characterizations for certain subclasses of Lipschitz spaces Lambda(center dot)beta(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\Lambda }}_{\beta }(\mathbb {G})$$\end{document} are given.
In this paper we investigate a boundedness of the Hardy-Littlewood maximal operator M in the variable Lebesgue spaces in the context locally compact abelian group. We show that the local Muckenhoupt condition implies ...
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In this paper we investigate a boundedness of the Hardy-Littlewood maximal operator M in the variable Lebesgue spaces in the context locally compact abelian group. We show that the local Muckenhoupt condition implies the local boundedness of M.
For any nonempty set U subset of R+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \set...
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For any nonempty set U subset of R+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U\subset {\mathbb {R}}<^>+$$\end{document}, we consider the maximal operator HU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}<^>U$$\end{document} defined as HUf=supu is an element of U|H(u)f|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}<^>Uf=\sup _{u\in U}|H<^>{(u)} f|$$\end{document}, where H(u)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>{(u)}$$\end{document} represents the Hilbert transform along the monomial curve u gamma(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u\gamma (s)$$\end{document}. We focus on the Lp(Rd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>p({\mathbb {R}}<^>d)$$\end{document} operator norm of HU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage
We study the boundedness of Hardy-Littlewood maximal function on the spaces defined in terms of Choquet integrals associated with weighted Bessel and Riesz capacities. As a consequence, we obtain a class of weighted S...
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We study the boundedness of Hardy-Littlewood maximal function on the spaces defined in terms of Choquet integrals associated with weighted Bessel and Riesz capacities. As a consequence, we obtain a class of weighted Sobolev inequalities.
We obtain bounds in full range of exponents for the Hardy-Littlewood maximal function on spaces defined via Choquet integrals associated to Bessel or Riesz capacities. We then deduce Sobolev type embeddings in these s...
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We obtain bounds in full range of exponents for the Hardy-Littlewood maximal function on spaces defined via Choquet integrals associated to Bessel or Riesz capacities. We then deduce Sobolev type embeddings in these spaces as a consequence.
We establish the strong L-p-inequality for the maximal function over hyper-surface based on Euclidean ball sup(t>0) 1/vertical bar B-n vertical bar integral(Bn)f(x - tu, y - t(2)vertical bar u vertical bar(2))du. W...
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We establish the strong L-p-inequality for the maximal function over hyper-surface based on Euclidean ball sup(t>0) 1/vertical bar B-n vertical bar integral(Bn)f(x - tu, y - t(2)vertical bar u vertical bar(2))du. We prove the L-p-boundedness of the maximal function for p > 1. Specially, when p = 2, we prove the L-2-boundedness of the maximal function can be controlled by Cn(7/8), where C is independent of n.
In this paper, we investigated the commutators of Hardy-Littlewood maximal function with symbol function b in generalized BMO spaces. Some characterizations of generalized BMO spaces are obtained via the strong and we...
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In this paper, we investigated the commutators of Hardy-Littlewood maximal function with symbol function b in generalized BMO spaces. Some characterizations of generalized BMO spaces are obtained via the strong and weak boundedness of the commutators on Orlicz-Morrey space.
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