Singular measures with smal H(p, q)-projections

Evgueni Doubtsov

doi:10.1007/BF02384774

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Home > Journals > Ark. Mat. > Volume 36 > Issue 2 > Article

October 1998 Singular measures with smal H(p, q)-projections

Evgueni Doubtsov

Author Affiliations +

Evgueni Doubtsov¹
¹Centre de Recerca Matemàtica, Institut d’Estudis Catalans

Ark. Mat. 36(2): 355-361 (October 1998). DOI: 10.1007/BF02384774

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Abstract

We construct a singular probability measure μ on the complex sphere such that the Poisson integral of μ is a pluriharmonic function in the ball and the Fourier transform of μ is $\mathcal{O}(1/\sqrt p )$ as p→∞.

Funding Statement

Supported by the Centre de Recerca Matemàtica (Institut d’Estudis Catalans, Barcelona) under a grant from DGICYT (Spain); partially supported by the RFFI grant 96-01-00693.