Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type

DOI10.1016/J.JMAA.2004.02.012zbMath1072.42013OpenAlexW1989023150MaRDI QIDQ596710

José Maria Martell

Publication date: 10 August 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.02.012

zbMATH Keywords

weightsspaces of homogeneous typeCalderón-Zygmund decompositionfractional integralspotential operatorsweak type inequalities

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Linear operators on function spaces (general) (47B38) Integral operators (47G10) Inequalities for sums, series and integrals (26D15)

Related Items (15)

Two-weight inequalities for commutators of potential operators on spaces of homogeneous type ⋮ Inequalities for the composition of Green's operator and the potential operator ⋮ Imbedding Inequalities for Composition of Green’s and Potential Operators ⋮ BMO and Lipschitz norm estimates for the composition of Green's operator and the potential operator ⋮ Two-weight norm inequalities for some fractional type operators related to Schrödinger operator on weighted Morrey spaces ⋮ Two-weight, weak-type norm inequalities for fractional integral operators and commutators on weighted Morrey and amalgam spaces ⋮ Integral Norm Inequalities for Various Operators on Differential Forms ⋮ Criteria of a multi-weight weak type inequality in Orlicz classes for maximal functions defined on homogeneous type spaces ⋮ Recent advances in \(L^p\)-theory of homotopy operator on differential forms ⋮ A weighted weak type estimate for the fractional integral operator on spaces of homogeneous type ⋮ Imbedding inequalities with \(L{\varphi}\)-norms for composite operators ⋮ Weighted inequalities for potential operators on differential forms ⋮ Weighted inequalities for potential operators with Lipschitz and BMO norms ⋮ Two-weight weak-type inequalities for potential type operators ⋮ Weighted estimates for commutators of potential operators on spaces of homogeneous type

Cites Work

• Unnamed Item
• Lipschitz functions on spaces of homogeneous type
• Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces
• A characterization of some weighted norm inequalities for the fractional maximal function
• Two-weight, weak-type norm inequalities for fractional integrals, Calderon-Zygmund operators
• Uncertainty principle estimates for vector fields

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