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Convolution Operators on Discrete Hardy Spaces
Author(s) -
Boza Santiago,
Carro María J.
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200106)226:1<17::aid-mana17>3.0.co;2-j
Subject(s) - mathematics , hardy space , convolution (computer science) , convolution power , pure mathematics , algebra over a field , mathematical analysis , fourier transform , fourier analysis , computer science , artificial intelligence , artificial neural network , fractional fourier transform
We establish the connection between the boundedness of convolution operators on H p (ℝ N ) and some related operators on H p (ℤ N ). The results we obtain here extend the already known for L p spaces with p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential type belonging to Hardy spaces