Littlewood–Paley operators and Sobolev spaces

Shuichi Sato

doi:10.1215/ijm/1446819299

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Home > Journals > Illinois J. Math. > Volume 58 > Issue 4 > Article

Winter 2014 Littlewood–Paley operators and Sobolev spaces

Shuichi Sato

Illinois J. Math. 58(4): 1025-1039 (Winter 2014). DOI: 10.1215/ijm/1446819299

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Abstract

We prove some weighted estimates for two kinds of Littlewood–Paley operators related to the Riesz potentials, which can be used to characterize the weighted Sobolev spaces. Also, we show the boundedness from the weighted Hardy space $H^{1}_{w}$ to the weighted weak $L^{1}$ space of a Littlewood–Paley operator arising from spherical means.

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Shuichi Sato. "Littlewood–Paley operators and Sobolev spaces." Illinois J. Math. 58 (4) 1025 - 1039, Winter 2014. https://doi.org/10.1215/ijm/1446819299