Weighted and vector-valued inequalities for potential operators

Ruiz Blasco, Francisco J.; Torrea Hernández, José L.

doi:10.1090/S0002-9947-1986-0831197-4

Weighted and vector-valued inequalities for potential operators
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by Francisco J. Ruiz Blasco and José L. Torrea Hernández PDF

Trans. Amer. Math. Soc. 295 (1986), 213-232 Request permission

Abstract:

In this paper we develop some aspect of a general theory parallel to the Calderón-Zygmund theory for operator valued kernels, where the operators considered map functions defined on ${R^n}$ into functions defined on $R_ + ^{n + 1} = {R^n} \times [0,\infty )$. In particular, we apply the obtained results to get vector-valued inequalities for the Poisson integral and fractional integrals. Some weighted norm inequalities are also considered for fractional integrals.

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