Conjugate function theory in weak1 Dirichlet algebras |
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Authors: | I.I. Hirschman Richard Rochberg |
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Affiliation: | Washington University, St. Louis, Missouri 63130 USA |
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Abstract: | The fundamental theorems on conjugate functions are shown to be valid for weak1 Dirichlet algebras. In particular the conjugation operator is shown to be a continuous map of Lp to Lp for 1 < p < ∞, to be a continuous map of L1 to Lp, 0 < p < 1, and to map functions in L∞ to exponentially integrable functions. These results allow a number of results for Dirichlet algebras to be extended to weak1 Dirichlet algebras. |
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