This paper is essentially the second author's lecture at the CIMPA School. It summarises large parts of the three authors'paper "On the H^1-L^1-boundedness of operators". Only one proof is given. In the setting of a Euclidean space, we consider operators defined and uniformly bounded on atoms of a Hardy space H^p. The question discussed is whether such an operator must be bounded on H^p. This leads to a study of the difference between countable and finite atomic decompositions in Hardy spaces.
Meda, S., Sjogren, P., Vallarino, M. (2009). Atomic decompositions and operators on Hardy spaces. REVISTA DE LA UNION MATEMATICA ARGENTINA, 50(2), 15-22.
Atomic decompositions and operators on Hardy spaces
MEDA, STEFANO;VALLARINO, MARIA
2009
Abstract
This paper is essentially the second author's lecture at the CIMPA School. It summarises large parts of the three authors'paper "On the H^1-L^1-boundedness of operators". Only one proof is given. In the setting of a Euclidean space, we consider operators defined and uniformly bounded on atoms of a Hardy space H^p. The question discussed is whether such an operator must be bounded on H^p. This leads to a study of the difference between countable and finite atomic decompositions in Hardy spaces.
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