On the ¹–¹ boundedness of operators

By S. Meda, P. Sjögren, Maria Vallarino. 2008

79 citations recorded by the source corpus.

We prove that if q is in (1,\infty), 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 which is uniformly bounded on (1,q)-atoms, 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 with continuous (1,\infty)-atoms. This is known to be false for (1,\infty)-atoms.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9779d6cf066dfef6e16a981251d07dffe25dc644

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In Applied Mathematics

1. Yuan Zhou
2. Dachun Yang
3. Wen Yuan
4. Luong Dang Ky
5. Pekka Koskela
6. Jun Liu
7. Sibei Yang
8. Yangyang Zhang

In Mathematical Physics

1. Dachun Yang
2. Yuan Zhou
3. Wen Yuan
4. Luong Dang Ky
5. Sibei Yang
6. Jun Liu
7. Marcin Bownik
8. Yangyang Zhang

Citations in the corpus

• Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\ (2009, background): “,fin(X). Then T0 satisfies (3.10). By Proposition 3.2, T0 has an extension, denoted by Te0, such that Te0 is bounded from H1 ρ(X) to L1(X). However, Te 0 may not coincide with Ton all (1,∞)ρ-atoms. See [3, 56, 39, 21] for further details and examples. (iv) As an replacement of (iii) of this remark, we”