Weighted inequalities and Stein-Weiss potentials

2006/07/13 by Beckner, William · 3 citations
#35A15 #42B10 #58J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0607309

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.

Cited by

• Asymptotically sharp Hardy-Rellich inequalities on lattices
• On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking
• On a fuzzy Landau Equation: Part II. Solvability results

Related

• Stein-Weiss inequality on product spaces
• On the end-point of Stein-Weiss inequality
• Pitt's inequality with sharp convolution estimates
• Pitt's inequality and the fractional Laplacian: sharp error estimates
• Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability