Fractional integrals on weighted 𝐻^{𝑝} spaces

Gatto, Angel E.; Gutiérrez, Cristian E.; Wheeden, Richard L.

doi:10.1090/S0002-9947-1985-0784004-1

Fractional integrals on weighted $H\sp p$ spaces

Authors: Angel E. Gatto, Cristian E. Gutiérrez and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 289 (1985), 575-589
MSC: Primary 42B30; Secondary 31B15, 46E35, 46F10
DOI: https://doi.org/10.1090/S0002-9947-1985-0784004-1
MathSciNet review: 784004
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Abstract: We characterize the pairs of doubling weights on ${R^n}$ such that

$\displaystyle \parallel {I_\alpha }f{\parallel _{H_u^q}} \leq c\parallel f{\parallel _{H_v^p}}, \quad 0 < p < q < \infty$

, where ${I_\alpha },\alpha > 0$ , is the fractional integral operator. We also consider the behavior of an associated maximal function. Applications of the results to Sobolev inequalities in weighted ${L^p}$ spaces are given.

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