Stein–Weiss inequalities for the fractional integral operators in Carnot groups and applications

DOI10.1080/17476930902999074zbMath1205.42023OpenAlexW1977679284MaRDI QIDQ4931836

A. Serbetci, Vagif S. Guliyev, Rza Ch. Mustafayev

Publication date: 1 October 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930902999074

zbMATH Keywords

fractional integral operatorStein-Weiss inequalitynilpotent stratified Lie group

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Analysis on other specific Lie groups (43A80) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (6)

Young's inequalities and Hausdorff-Young inequalities on Herz spaces ⋮ Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups ⋮ Stein-Weiss-Adams inequality on Morrey spaces ⋮ Stein-Weiss inequalities for radial local Morrey spaces ⋮ Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups ⋮ A survey of Hardy type inequalities on homogeneous groups

Cites Work

• Inégalités de Sobolev produit sur les groupes de Lie nilpotents. (Product Sobolev inequalities on nilpotent Lie groups)
• Sobolev inequalities on Lie groups and symmetric spaces
• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Analysis on nilpotent groups
• Besov spaces and Sobolev spaces on a nilpotent Lie group
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• Analysis on the Heisenberg group and estimates for functions in Hardy classes of several complex variables
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Hypoelliptic second order differential equations
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Besov Spaces and Hausdorff Dimension For Some Carnot-Carathéodory Metric Spaces
• Littlewood–Paley decompositions and Besov spaces on Lie groups of polynomial growth
• A fundamental solution for a subelliptic operator

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