一类极大球形和算子的幂权范数不等式

NORM INEQUALITY WITH POWER WEIGHTS FOR A CLASS OF MAXIMAL SPHERICAL SUMMATION OPERATORS

设{R_l}为 Hadamard 缺项序列,σ_R~δ(f)为 f 的 Fourier 变换的δ阶 Bochner-Riesz 平均,证明了若0≤δ<1/2(n-1)及|α|<1+2δ,则有■(sup|σ_(Rj)~δ(f)(x)|)~2|x|~αdx≤c■|f(x)|~2|x|~αdx,其中常数 c 与 f 无关.

Let{R_z}be Hadamard's lacunary sequence,and σ_R~δ_R(f) be the Bochner- Riesz means with δ order for the Fourier transform of f(x).It is proved that if 0≤δ<(n-1)/2 and|α|<1+2δ then the inequality■(sup|σ_(Rj)~δ(f)(x)|)~2 ·|x|~αdx≤c■|f(x)|~2|x|~αdx holds.