Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials. (English) Zbl 0941.42006
This paper presents results about parabolic singular integrals with rough kernels that extend previous work of J. Lewis and M. Murray on layer potentials for the heat equation in time-varying domains. The precise relations between the Lewis-Murray work and the author’s work was described in my review of [S. Hofmann, Contemp. Math. 189, 251-285 (1995)] in Zbl 0883.42015. The techniques used here are similar to those of the latter paper, where the author says “Indeed, we had found the results of the present paper first, and then had pushed those methods to include the “nonlinear” operators of the paper under review”. The results are too technical to be described in detail but again involve replacement of the \(T1\) theorem via Littlewood-Paley estimates and a quasi-Carleson measure condition. The operators considered include nonlinear ones but the commutators are more restricted, satisfying a cancellation condition.
Reviewer: R.Johnson (College Park)
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
Keywords:
parabolic singular integrals; rough kernels; \(T1\) theorem; Littlewood-Paley estimates; quasi-Carleson measureCitations:
Zbl 0883.42015References:
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