Czechoslovak Mathematical Journal, Vol. 69, No. 2, pp. 337-351, 2019


Boundedness of Littlewood-Paley operators relative to non-isotropic dilations

Shuichi Sato

Received June 28, 2017.   Published online August 6, 2018.

Abstract:  We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $\Bbb R^n$. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^p$ spaces, $1<p<\infty$, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).\looseness-1
Keywords:  Littlewood-Paley function; non-isotropic dilation
Classification MSC:  42B25, 46E30
DOI:  10.21136/CMJ.2018.0313-17


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Affiliations:   Shuichi Sato, Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa 920-1192, Japan, e-mail: shuichi@kenroku.kanazawa-u.ac.jp


 
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