The bilinear Bochner-Riesz problem
نویسندگان
چکیده
منابع مشابه
The bilinear Bochner-Riesz problem
Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers (1 − |ξ| − |η|)+ and we make some advances in this investigation. We obtain an optimal result concerning the boundedness of these means from L × L into L with minimal smoothness, i.e., any δ > 0, and we obtain estimates for other pairs of spaces for...
متن کاملImproved Bounds for Bochner-riesz and Maximal Bochner-riesz Operators
In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.
متن کاملA Proof of the Bochner-riesz Conjecture
For f ∈ S(R), we consider the Bochner-Riesz operator R of index δ > 0 defined by R̂δf(ξ) = (1− |ξ|)+ f̂(ξ). Then we prove the Bochner-Riesz conjecture which states that if δ > max{d|1/p − 1/2| − 1/2, 0} and p > 1 then R is a bounded operator from L(R) into L(R); moreover, if δ(p) = d(1/p − 1/2) − 1/2 and 1 < p < 2d/(d + 1), then Rδ(p) is a bounded operator from L(R) into L(R).
متن کاملANALYSIS 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...
متن کاملSpectra of Bochner-Riesz means on L
The Bochner-Riesz means are shown to have either the unit interval [0, 1] or the whole complex plane as their spectra on Lp, 1 ≤ p <∞
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2015
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-015-0028-y