A family of strongly singular operators

Journal of the Australian Mathematical Society

Magali Folch-Gabayet¹ 

关键词: primary 42A45;    42A85;    43A32;    44A05;    44A35;   

DOI  :  10.1017/S1446788700000872

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let ψ be a positive function defined near the origin such lim1 →0+ ψ(t) = 0. We consider the operator Tzƒ, defined as the pricipal value of the convolution of function ƒ and a kernel K(t) = eiy(t)t−z /ψ(t)1−z, where z is a complex number, 0 ≤ Re(z) ≤ 1, 0 < t ≤ 1 and γ is a real function. Assuming certain regularity conditions on ψ and γ and certain relations between ψ and γ we show that Tθ is a bounded operator on Lp (R) for 1/p = (1+ θ) /2 and 0 ≤ θ < 1, and T1 is bounded from H1 (R) to L1 (R).

【 授权许可】

Unknown