ANALYSIS CLUB Bochner-Riesz Multipliers
نویسنده
چکیده
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 smoother hence more likely to produce a bounded operator. The main references for the following discussion are [2, Ch 8, §5] and [1, pp143-157].
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