Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 57, Number 4 (2005), 1129-1152.
Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds
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 .
J. Math. Soc. Japan, Volume 57, Number 4 (2005), 1129-1152.
First available in Project Euclid: 14 June 2006
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DUONG, Xuan Thinh; YAN, Lixin. Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds. J. Math. Soc. Japan 57 (2005), no. 4, 1129--1152. doi:10.2969/jmsj/1150287306. https://projecteuclid.org/euclid.jmsj/1150287306