Calderón–Zygmund Kernels and Boundary Estimates

Kazuaki Taira ()
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Kazuaki Taira: University of Tsukuba, The College of Mathematics

Chapter Chapter 14 in Real Analysis Methods for Markov Processes, 2024, pp 435-479 from Springer

Abstract: Abstract The purpose of this chapter is to prove the global a priori estimate (12.3) for the homogeneous Dirichlet problem stated in Theorem 12.2 (see [35, Theorem 4.2]). The desired global a priori estimate (12.3) is a consequence of the explicit boundary representation formula (14.2) for the solutions of the homogeneous Dirichlet problem and an $$L^{p}$$ L p boundedness of some singular integral operators and boundary commutators in the boundary representation formula (14.2) (Theorems 14.2 and 14.5).

Date: 2024
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DOI: 10.1007/978-981-97-3659-1_14

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