Sharp weighted bounds for fractional integral operators
Copyright policy )Sharp weighted bounds for fractional integral operators
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.
v2: changes made to reflect referee's report. Final version of the paper. To appear in J Func Anal
- University of Seville Spain
- Universidad de Sevilla (US) Spain
- University of Seville Spain
- University of Kansas United States
- University of Kansas Center for Research Inc United States
Maximal functions, Littlewood-Paley theory, Extrapolation, extrapolation, fractional integrals, Weighted norm inequalities, Extrapolació, weighted norm inequalities, Classical Analysis and ODEs (math.CA), FOS: Mathematics, sharp bounds, 42B20, 42B25, fractional integral, Maximal operators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Fractional integrals, Singular integrals, 517 - Anàlisi, Sharp bounds, Functional Analysis (math.FA), Mathematics - Functional Analysis, Integrals fraccionàries, Mathematics - Classical Analysis and ODEs, singular integrals, Analysis, Integrals singulars
Maximal functions, Littlewood-Paley theory, Extrapolation, extrapolation, fractional integrals, Weighted norm inequalities, Extrapolació, weighted norm inequalities, Classical Analysis and ODEs (math.CA), FOS: Mathematics, sharp bounds, 42B20, 42B25, fractional integral, Maximal operators, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Fractional integrals, Singular integrals, 517 - Anàlisi, Sharp bounds, Functional Analysis (math.FA), Mathematics - Functional Analysis, Integrals fraccionàries, Mathematics - Classical Analysis and ODEs, singular integrals, Analysis, Integrals singulars
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