Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means

Endpoint Inequalities for Bochner-riesz Multipliers in the Plane

A weak-type inequality is proved for Bochner-Riesz means at the critical index, for functions in L(R), 1 ≤ p < 4/3.

ANALYSIS CLUB Bochner-Riesz Multipliers

We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...

Eigenfunction and Bochner Riesz Estimates on Manifolds with Boundary

Endpoint Bilinear Restriction Theorems for the Cone, and Some Sharp Null Form Estimates

for some integer k. In both cases we call 2 the frequency of the waves φ, ψ. Red and blue waves both solve the free wave equation, but propagate along different sets of characteristics. Note that blue waves are the time reversal of red waves. Also, these waves are automatically smooth thanks to the frequency localization. The vector valued formulation will be convenient for technical reasons. W...

The Sharp Riesz Potential Estimates in Metric Spaces

We introduce the Riesz potential operator for functions deened on a quasi-metric space endowed with a nonnegative doubling measure satisfying certain lower bound for the measure of a ball. For this operator we prove sharp Lorentz-norm estimates in the spirit of the results due to O'Neil and Peetre (in the non-limiting case) and to Hansson and Brrzis{Wainger (in the limiting case). One of the fo...