Boundedness of Operators over $$({\mathbb{R}}^{D},\mu )$$

Abstract

AbstractIn this chapter, we focus our attention on the boundedness of singular integral operators in the Lebesgue space and the Hardy space over \(({\mathbb{R}}^{D},\mu )\). We first establish some weighted estimates for local sharp maximal operator as well as several interpolation results which are useful in applications. Then we investigate the boundedness of singular integral operators on L p(μ) and H 1(μ), and the boundedness of maximal singular integral operators and commutators on L p(μ) as well as their endpoint estimates.KeywordsHardy SpaceMaximal OperatorLebesgue SpaceSingular Integral OperatorZygmund OperatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.