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Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces.
- Source :
-
Acta Mathematica Sinica . Sep2007, Vol. 23 Issue 9, p1537-1552. 16p. - Publication Year :
- 2007
-
Abstract
- In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral $$ \mu ^{\rho }_{{\Omega ,S}} $$ is a bounded operator from the Hardy space H 1(ℝ n ) to L 1(ℝ n ) and from the weak Hardy space H 1,∞(ℝ n ) to L 1,∞(ℝ n ), respectively. As corollaries of the above results, it is shown that $$ \mu ^{\rho }_{{\Omega ,S}} $$ is also an operator of weak type (1, 1) and of type ( p, p) for 1 < p < 2, respectively. These conclusions are substantial improvement and extension of some known results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *INTEGRALS
*HARDY spaces
*FUNCTIONAL analysis
*FUNCTION spaces
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 23
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 25946686
- Full Text :
- https://doi.org/10.1007/s10114-005-0912-y