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- W3204286334 abstract "The aim of this paper is to introduce and investigative some new function classes of Morrey–Campanato type. The domains $$Omega subset {mathbb {R}}^n$$ in this paper are supposed to satisfy the following property: there exists a constant $$A>0$$ such that for all $$x_{0}in Omega , rho <mathrm{diam} Omega $$ , we have $$|Q(x_{0},rho )cap Omega |ge Arho ^n.$$ Let $$0<p<infty $$ and $$0le lambda le n+p$$ . We say that $$fin bar {mathcal{L}}^{p,lambda }(Omega )$$ if $$begin{aligned} sup _{x_{0}in Omega ,rho >0}rho ^{-lambda }int _{Omega (x_{0},rho )}big |f(x)-|f|_{Omega (x_{0},rho )}big |^p {mathrm{d}}x<infty , end{aligned}$$ where $$Omega (x_{0},rho )=Q(x_{0},rho )cap Omega $$ and $$Q(x,rho )$$ is denote the cube of $${mathbb {R}}^n$$ . Some basic properties and characterizations of these classes are presented. If $$0le lambda <n$$ , the space is equivalent to related Morrey space under certain conditions. If $$lambda =n$$ , then $$f in bar {mathcal{L}}^{p,n}(Omega )$$ if and only if $$fin {mathrm{BMO}}(Omega )$$ with $$f^{-}in L^{infty }(Omega )$$ , where $$f^{-}=-min {0,f}$$ . If $$n<lambda le n+p$$ , the $$bar {mathcal{L}}^{p,lambda }(Omega )$$ functions establish an integral characterization of the nonnegative Hölder continue functions. As applications, this paper gives unified criteria on the necessity of bounded commutators of maximal functions on ball Banach function spaces." @default.
- W3204286334 created "2021-10-11" @default.
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- W3204286334 date "2022-05-18" @default.
- W3204286334 modified "2023-10-18" @default.
- W3204286334 title "New function classes of Morrey–Campanato type and their applications" @default.
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- W3204286334 doi "https://doi.org/10.1007/s43037-022-00193-7" @default.
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