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arXiv · 0906.2666

Square function and Riesz transform in non-integer dimensions

Svitlana Mayboroda·Alexander Volberg
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Abstract

Following a recent paper by X. Tolsa and A. Ruiz de Villa [Non existence of principal values of signed Riesz transforms of non integer dimension, preprint], we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure $H^s$ implies that $s$ is integer.

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Svitlana Mayboroda, Alexander Volberg. 2009-06-15. Square function and Riesz transform in non-integer dimensions. https://doi.org/10.1016/j.crma.2009.09.020

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