广义Morrey空间与广义Campanato.pdf

40v1 C n n Vol.40, No. 1 19971 ACTA MATHEMATICA SINICA Jan., 1997 C Morrey GC Campanato EF (I) pUvh (JDsoDoX J 150001) I Campanato czgmZRjxYXuwnSOokd Morrey c Campanato cPrbdtiXs Morrey cs Campanato cX qeouws Campanato cWVdfTQlygmZRaXq s Morrey cs Campanato cq MR(1991) M 46B20, 46N20 L O177.92 Generalized Morrey Space and Generalized Campanato Space and Their Application (I) Wu Congxin Fu Yongqiang (Department of Mathematics, Harbin Institute of Technology, Harbin 150008, China) Abstract Campanato space is widely used to study partial differential equation. Thus in this paper we generalize Morrey space and Campanato space, and study the proper- ties of the introduced generalized Morrey space and generalized Campanato space. In another paper, we obtain the regularity for nonpower growth elliptic partial differential equation by means of generalized Campanato space. Keywords Generalized Morrey space, Generalized Campanato space, Regularity 1991 MR Subject Classification 46B20, 46N20 Chinese Library Classification O177.92 John-Nirenberg[1] Morrey aewP Campanato WLpte a Campanato a [2] qwP Campanato aF QlfptvOe [3] VxSS NF Morrey aL Campanato aRhrptceaf TkIr Morrey aL Campanato akIwPTfF Campanato a QlfptZeOeQ div (ψ (|Du|)Du) = 0, ψ RfKAeOeQptTfkM Orlicz aNF Campanato alfuIYjTfPS C B 1994-10-13, gA 1996-04-22, i 1996-05-24 HyoSoa UG Morrey bG Campanato bW (I) 123 1 HK dnSV Orlicz atbuIze [4] R [5]. S Ω R Rn mwU Ω(x, ρ) = B (x, ρ) ∩ Ω, B (x, ρ) Rw x Rd sR ρ B 1.1 T R1 KA M (u) R N KAIHuZf 1. M (u) RkMKA M (0) = 0; 2. u 0 M