Abstract
Let be a space of homogeneous type. Assume that has a bounded holomorphic functional calculus on and generates a semigroup with suitable upper bounds on its heat kernels where is a measurable subset of . For appropriate bounded holomorphic functions , we can define the operators on , . We establish conditions on positive weight functions such that for each , , there exists a constant such that for all .
Applications include two-weight inequalities for Schrödinger operators with non-negative potentials on and divergence form operators on irregular domains of .
Citation
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
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