Differentiability and Holder continuity of Riesz potentials of Orlicz functions
Differentiability and Holder continuity of Riesz potentials of Orlicz functions
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Orlicz 函数 Riesz 势的可微性和 Holder 连续性
DOI：
10.1524/anly.2000.20.3.201
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发表时间：
2000
影响因子：
2.4
通讯作者：
T. Shimomura
中科院分区：
文献类型：
--
作者：
Y. Mizuta;T. Shimomura
对于每个χ€RTM，其中m是正整数且1 < ρ < oo。更一般地，u€W（R”）有一个连续的代表u*，其偏导数小于m - n / p阶，且满足Holder条件。通过第一作者[7]，[9]的积分表示定理，将Sobolev函数表示为Riesz型势，并将上述Sobolev定理推广到Riesz势空间（参见[10，Section 4.2]）。对于贝塞尔势空间，我们请读者参考Adams-Hedberg[2，定理1.2.4和第3.7.3节]。a阶的Riesz势Raf由u*(x + h) - u*(x) = 0（\h\~/）定义为/i - >
for every χ € RTM, where m is a positive integer and 1 < ρ < oo. More generally, u € W(R") has a continuous representative u* whose partial derivatives of order less than m — n / p exist and satisfy the Holder condition. By the integral representation theorems of the first author [7], [9], Sobolev functions are represented as Riesz-type potentials, and Sobolev's theorem mentioned above is extended to the Riesz potential space (cf. [10, Section 4.2]). For the Bessel potential space, we refer the reader to Adams-Hedberg [2, Theorems 1.2.4 and Section 3.7.3]. The Riesz potential Raf of order a is defined by u*(x + h) — u*(x) = 0(\h\~/) as /i —> 0