Square function and Riesz transform in non-integer dimensions

Details Square function and Riesz transform in non-integer dimensions Square function and Riesz transform in non-integer dimensions

2009-06-15

arxiv.org/abs/0906.2666v1

Comptes rendus - Mathematique 347 (2009), pp. 1271-1276, http://dx.doi.org/10.1016/j.crma.2009.09.020

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1016/j.crma.2009.09.020

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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