Extrapolation Theorem And Operator Boundedness Estimation On Gaussian Measure Space

The emergence of the concept of non-double measure makes operator weighting inequality and operator theory have a new development direction.The weight theory under non-double measure is widely applied to operator theory and function space theory on non-double measure space.In this paper,we study the weighted norm inequality of local weight theory in Gaussian measure space.The extrapolation theorem is one of the most profound results in the study of weighted norm inequality in harmonic analysis.We get various forms of extrapolation theorem in Gaussian measure space and with the development of real analysis method,The classical concepts of the Littlewood-Paley theory can be extended beyond the Euclidean space setting.The bounded property of the Littlewood-Paley g operator is obtained.In Chapter 1,introduces the research background and related knowledge of this paper,mainly involving the following aspects:Weighted Inequality and extrapolation theorem;local weight theory Ap of Gaussian measure space;Littlewood-Paley theory;brief introduction of the main research contents of this paper.In Chapter 2,under the background of introducing Ap,a weights and Ap,q,a weights in Gaussian measure space,by using the double property of the suitable sphere in Gaussian measure space,we construct the appropriate A1,a weights through the Local Hardy-Littlewood maximal operator,and obtain the extrapolation theorem in Gaussian measure space by combining with the skills of proving the classical extrapolation theorem.In Chapter 3,assuming that Littlewood-Paley g function is bounded on L2(d?),we prove that Littlewood-Paley g function is bounded from L1(d?)to L1,?(d?)by using CZ decomposition under non doubling measure.