Boundedness of fractional operators on $L^{p}$ spaces with different weights
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- by Eleonor Harboure, Roberto A. Macías and Carlos Segovia PDF
- Trans. Amer. Math. Soc. 285 (1984), 629-647 Request permission
Abstract:
Let ${T_\alpha }$ be either the fractional integral operator $\smallint f(y)|x - y{|^{\alpha - n}}\; dy$, or the fractional maximal operator $\sup \left \{ {{r^{\alpha - n}}{\smallint _{|x - y| < r}}|f(y)|dy: r > 0} \right \}$. Given a weight $w$ (resp. $\upsilon$), necessary and sufficient conditions are given for the existence of a nontrivial weight $\upsilon$ (resp. $w$) such that ${(\smallint |{T_\alpha }f{|^q}\upsilon \;dx)^{1/q}} \leqslant {(\smallint |f{|^p}w\;dx)^{1/p}}$ holds. Weak type substitutes in limiting cases are considered.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 285 (1984), 629-647
- MSC: Primary 26D10; Secondary 42B25, 47B38
- DOI: https://doi.org/10.1090/S0002-9947-1984-0752495-7
- MathSciNet review: 752495