Abstract
In this article we develop the theory of one-sided versions of the g function of Littlewood and Paley, the area function S of Lusin and the\(g_\lambda ^* \) that admit weighted norm estimates with weights belonging to the classes A +p of Sawyer. In Sections 1 and 2 we give definitions and some lemmas that shall be needed. Section 3 is devoted to the study of the one-sided version of the functions g and S. In Section 4 we obtain a good λ estimate for the one-sided\(g_\lambda ^* \) function, and in Sections 5 and 6 we apply the results already obtained to fractional integrals and multiplier operators.
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The authors were supported by a grant from Consejo Nacional de Investigaciones Cientificas y Técnicas, Argentina.
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de Rosa, L., Segovia, C. One-sided Littlewood-Paley theory. The Journal of Fourier Analysis and Applications 3 (Suppl 1), 933–957 (1997). https://doi.org/10.1007/BF02656497
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DOI: https://doi.org/10.1007/BF02656497