Magnetic Hardy inequalities with singular integral weights
Hynek Kovarik, Pier Cristoforo Rossaro
TL;DR
This paper establishes Hardy inequalities for magnetic Dirichlet forms with singular integral weights, analyzing their optimality and applying findings to spectral estimates of magnetic Schrödinger operators.
Contribution
It introduces new Hardy inequalities involving magnetic Dirichlet forms with singular weights and explores their optimality and applications.
Findings
Derived Hardy inequalities for magnetic Dirichlet forms with singular weights
Analyzed local and global optimality of the integral weights
Applied results to spectral estimates for magnetic Schrödinger operators
Abstract
In this paper we present Hardy type inequalities for magnetic Dirichlet forms with singular integral weights. We analyze the local and global optimality of the integral weight and discuss several examples in details. An application of our results to spectral estimates for magnetic Schr\"odinger operators is provided as well.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Spectral Theory in Mathematical Physics