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Sobolev spaces with non-isotropic dilations and square functions of Marcinkiewicz type

Shuichi Sato Studia Mathematica MSC: Primary 42B25; Secondary 46E35. DOI: 10.4064/sm210819-19-3 Published online: 24 June 2022

Abstract

We consider the weighted Sobolev spaces associated with non-isotropic dilations of Calderón–Torchinsky and characterize the spaces by the square functions of Marcinkiewicz type including those defined with repeated uses of averaging operation.

Authors

  • Shuichi SatoDepartment of Mathematics
    Faculty of Education
    Kanazawa University
    Kanazawa 920-1192, Japan
    e-mail

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