Pseudodifferential Operators on Local Hardy Spaces |
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Authors: | J. Hounie Rafael Augusto dos Santos Kapp |
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Affiliation: | 1. Departamento de Matemática, Universidad Federal de S?o Carlos, S?o Carlos, SP, 13565-905, Brazil
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Abstract: | In this work, we study the continuity of pseudodifferential operators on local Hardy spaces h p (ℝ n ) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S 1,δ 0(ℝ n ), 0≤δ<1, and in some subclasses of S 1,10(ℝ n ) are bounded on h p (ℝ n ) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂ t +ib(x,t)∂ x , b(x,t)≥0, in spaces of mixed norm involving Hardy spaces. Work supported in part by CNPq, FINEP, and FAPESP. |
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Keywords: | Pseudodifferential operators Hardy spaces Local solvability |
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