Weighted inequalities and Stein-Weiss potentials
William Beckner
TL;DR
This paper extends classical inequalities like Pitt's and Hardy-Rellich by deriving sharp bounds for Stein-Weiss fractional integrals, incorporating gradient and vector-valued operators.
Contribution
It provides new sharp inequalities and bounds for Stein-Weiss potentials, including gradient forms and vector-valued operators, extending classical results.
Findings
Sharp Pitt's inequality extensions
Bounds for Stein-Weiss fractional integrals
Inclusion of Hardy-Rellich inequalities
Abstract
Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research · Mathematical functions and polynomials