Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in L^p

2011/10/25 by Boros, Nicholas, Volberg, Alexander · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1110.5405

Abstract

We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form of a vector acting on a scalar function. Using this technique we compute the sharp lower bound estimate for L^p operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator. Secondly, we consider matrix-valued multipliers to obtain a new proof showing that the L^p operator norm of the Ahlfors-Beurling operator is bounded below by p^*-1.

Cited by

• Korn's inequality from the viewpoint of calculus of variations
• Martingales, laminates and minimal Korn inequalities

Related

• Multi-linear operators given by singular multipliers
• The L^p-Operator Norm of a Quadratic Perturbation of the Real Part of\n the Ahlfors--Beurling Operator
• On Hermite pseudo-multipliers
• Some Optimizations for (Maximal) Multipliers in L^p
• On bandlimited multipliers on matrix-weighted L^p-spaces