A supercritical estimate for Bessel potentials on Lorentz spaces

被引：0
作者：
Chen, You-Wei [1 ]
机构：
[1] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu, Taiwan
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 28卷 / 02期
关键词：
Bessel potential; Lorentz space; Fractional integration inequality;
D O I：
10.1007/s00030-021-00675-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we give a simple proof of an estimate for Bessel potentials acting on Lorentz spaces in the supercritical exponent: let 1 < p = d/alpha-1 and 1 <= q <= +infinity. If f is an element of L-p,L-q (R-d), then there exists a constant C = C(alpha, d, p, q) such that vertical bar g(alpha) * f(x) - g(alpha) * f(z)vertical bar <= C vertical bar x - z| (vertical bar ln(vertical bar x - z vertical bar)vertical bar + 1)1/q' parallel to f parallel to (Lp,q).
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页数：27
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