HAUSDORFF OPERATORS OVER DOUBLE COSET SPACES OF GROUPS WITH LOCALLY DOUBLING PROPERTY

摘要

Abstract We consider the boundedness of Hausdorff operators on the real Hardy spaces H1documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$H^{1}$$end{document} over double coset spaces of locally compact groups with the local doubling property and approximate midpoint property. The Lqdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^{q}$$end{document} spaces as well as the example of the group of Euclidean motions are also considered.