Coefficient Condition forL1-Convergence of Walsh–Fourier Series |
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Authors: | S. Fridli |
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Affiliation: | Department of Numerical Analysis, Eötvös L. University, 1088, Budapest, Muzeum krt. 6-8, Hungary |
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Abstract: | In this paper we give a condition with respect to Walsh–Fourier coefficients that implies theL1-convergence of the corresponding Walsh–Fourier series. We show that theL1-convergence class induced by this condition contains each one of the previously known convergence classes as a proper subset. We also show that our condition implies not only theL1-convergence but also the convergence in the dyadic Hardy norm if the function represented by the series belongs to the dyadic Hardy space. |
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