scholarly journals Spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

2011 ◽  
Vol 63 (1) ◽  
pp. 295-319 ◽  
Author(s):  
Xuan Thinh DUONG ◽  
Lixin YAN
Keyword(s):  
Hardy Spaces ◽  
Spectral Multipliers ◽  
Adjoint Operators

scholarly journals Spectral Multipliers of Self-Adjoint Operators on Besov and Triebel–Lizorkin Spaces Associated to Operators

2019 ◽  
Author(s):  
The Anh Bui ◽  
Xuan Thinh Duong
Keyword(s):  
Heat Kernel ◽  
Hardy Spaces ◽  
Adjoint Operator ◽  
Space Of Homogeneous Type ◽  
Multiplier Theorem ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Gaussian Estimate ◽  
Adjoint Operators

Abstract Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ that satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Hörmander-type spectral multiplier theorem for $L$ on the Besov and Triebel–Lizorkin spaces associated to $L$. Our work not only recovers the boundedness of the spectral multipliers on $L^p$ spaces and Hardy spaces associated to $L$ but also is the 1st one that proves the boundedness of a general spectral multiplier theorem on Besov and Triebel–Lizorkin spaces.

scholarly journals Local Hardy Spaces with Variable Exponents Associated with Non-negative Self-Adjoint Operators Satisfying Gaussian Estimates

2019 ◽  
Vol 30 (3) ◽  
pp. 3275-3330 ◽  
Author(s):  
Víctor Almeida ◽  
Jorge J. Betancor ◽  
Estefanía Dalmasso ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Local Hardy Spaces ◽  
Adjoint Operators ◽  
Gaussian Estimates

scholarly journals WEIGHTED HARDY SPACES ASSOCIATED TO SELF-ADJOINT OPERATORS AND $BMO_{L,w}$

2014 ◽  
Vol 18 (5) ◽  
pp. 1663-1678 ◽  
Author(s):  
Suying Liu ◽  
Kai Zhao ◽  
Shujuan Zhou
Keyword(s):  
Hardy Spaces ◽  
Weighted Hardy Spaces ◽  
Adjoint Operators

scholarly journals Notes on boundedness of spectral multipliers on Hardy spaces associated to operators

2011 ◽  
Vol 203 ◽  
pp. 109-122
Author(s):  
Bui The Anh
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Analytic Semigroup ◽  
Adjoint Operator ◽  
Upper Bounds ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Spectral Multipliers ◽  
Spectral Multiplier ◽  
Suitable Function

AbstractLetLbe a nonnegative self-adjoint operator onL2(X), whereXis a space of homogeneous type. Assume thatLgenerates an analytic semigroupe–tlwhose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplierF(L) is bounded onfor 0< p< 1, the Hardy space associated to operatorL, whenFis a suitable function.

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