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October, 2005 Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds
Xuan Thinh DUONG, Lixin YAN
J. Math. Soc. Japan 57(4): 1129-1152 (October, 2005). DOI: 10.2969/jmsj/1150287306

Abstract

Let 𝒳 be a space of homogeneous type. Assume that L has a bounded holomorphic functional calculus on L 2 ( Ω ) and L generates a semigroup with suitable upper bounds on its heat kernels where Ω is a measurable subset of 𝒳 . For appropriate bounded holomorphic functions b , we can define the operators b ( L ) on L p ( Ω ) , 1 p . We establish conditions on positive weight functions u , v such that for each p , 1 < p < , there exists a constant c p such that Ω | b ( L ) f ( x ) | p u ( x ) d μ ( x ) c p | | b | | p Ω | f ( x ) | p v ( x ) d μ ( x ) for all f L p ( v d μ ) .

Applications include two-weight L p inequalities for Schrödinger operators with non-negative potentials on R n and divergence form operators on irregular domains of R n .

Citation

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Xuan Thinh DUONG. Lixin YAN. "Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds." J. Math. Soc. Japan 57 (4) 1129 - 1152, October, 2005. https://doi.org/10.2969/jmsj/1150287306

Information

Published: October, 2005
First available in Project Euclid: 14 June 2006

zbMATH: 1084.42010
MathSciNet: MR2183586
Digital Object Identifier: 10.2969/jmsj/1150287306

Subjects:
Primary: 42B20 , 42B25 , 47B38

Keywords: elliptic operator , holomorphic functional calculus , semigroup kernel , singular integral operator , space of homogeneous type , weights‎

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 4 • October, 2005
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