The singular integral operators related to generalized shift operator in Hardy spaces

This thesis consists of six chapters. In the first chapter, summary of the classical Hardy spaces and its history is given. The second chapter is devoted to some basic concepts related to the topic. In chapter 3, by introducing the general information of singular integral operators, the most important one of them Riesz transforms are given. In chapter 4, the definition of real variable Hardy spaces associated with the Laplace-Bessel differential operator is given. Here, by introducing the definition of maximal functions related to Laplace-Bessel differential operator, the characterization of this maximal function is examined in $ H_{\triangle_{\nu}}^{p}$ Hardy space. As a result, for $p>1$ the relationship between $ H_{\triangle_{\nu}}^{p}$ Hardy spaces with $L^{p}_{\nu}$ Lebesgue space is given. In chapter 5, the theorem related to boundedness of high order Riesz-Bessel transforms associated to the Laplace-Bessel differential operator generated by generalized shift shift operator is given in $ H_{\triangle_{\nu}}^{p}$ Hardy space. To prove this theorem, the atomic decomposition of the $ H_{\triangle_{\nu}}^{p}$ Hardy space is used . Thus, for $0Keyword: Analiz = Analysis