A spectral multiplier theorem for Hardy spaces associated with Schrödinger operator on the Heisenberg group

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Nan Hu ◽  
Jiman Zhao
Keyword(s):  
Heisenberg Group ◽  
Schrödinger Operator ◽  
Hardy Spaces ◽  
Schrodinger Operator ◽  
Multiplier Theorem ◽  
Spectral Multiplier

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 Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hua Zhu
Keyword(s):  
Schrödinger Operator ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Nonnegative Function ◽  
Riesz Transforms ◽  
Schrodinger Operator ◽  
Weighted Hardy Spaces ◽  
Local Hardy Spaces ◽  
Reverse Hölder

We characterize the weighted local Hardy spaceshρ1(ω)related to the critical radius functionρand weightsω∈A1ρ,∞(Rn)by localized Riesz transformsR^j; in addition, we give a characterization of weighted Hardy spacesHL1(ω)via Riesz transforms associated with Schrödinger operatorL, whereL=-Δ+Vis a Schrödinger operator onRn(n≥3) andVis a nonnegative function satisfying the reverse Hölder inequality.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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