We prove that if q is in (1,∞), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R^n with the property that sup{TaY : a is a (1, q)-atom} < ∞, then T admits a (unique) continuous extension to a bounded linear operator from H^1(R^n) to Y . We show that the same is true if we replace (1, q)-atoms by continuous (1,∞)-atoms. This is known to be false for (1,∞)-atoms.
On the H^1-L^1-boundedness of operators / Meda, S; Sjogren, P; Vallarino, Maria. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 136:(2008), pp. 2921-2931.
On the H^1-L^1-boundedness of operators
VALLARINO, MARIA
2008
Abstract
We prove that if q is in (1,∞), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R^n with the property that sup{TaY : a is a (1, q)-atom} < ∞, then T admits a (unique) continuous extension to a bounded linear operator from H^1(R^n) to Y . We show that the same is true if we replace (1, q)-atoms by continuous (1,∞)-atoms. This is known to be false for (1,∞)-atoms.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2386657