ﻻ يوجد ملخص باللغة العربية
Let $nge2$ and $phi : [0,fz) to [0,infty)$ be a Youngs function satisfying $sup_{x>0} int_0^1frac{phi( t x)}{ phi(x)}frac{dt}{t^{n+1} }<infty. $ We show that Ahlfors $n$-regular domains are Besov-Orlicz ${dot {bf B}}^{phi}$ extension domains, which is necessary to guarantee the nontrivially of ${dot {bf B}}^{phi}$. On the other hand, assume that $phi$ grows sub-exponentially at $fz$ additionally. If $Omega$ is a Besov-Orlicz ${dot {bf B}}^{phi}$ extension domain, then it must be Ahlfors $n$-regular.
In this paper we build up a criteria for fractional Orlicz-Sobolev extension and imbedding domains on Ahlfors $n$-regular domains.
The paper puts forward new Besov spaces of variable smoothness $B^{varphi_{0}}_{p,q}(G,{t_{k}})$ and $widetilde{B}^{l}_{p,q,r}(Omega,{t_{k}})$ on rough domains. A~domain~$G$ is either a~bounded Lipschitz domain in~$mathbb{R}^{n}$ or the epigraph of a
We prove that a bi-Lipschitz image of a planar $BV$-extension domain is also a $BV$-extension domain, and that a bi-Lipschitz image of a planar $W^{1,1}$-extension domain is again a $W^{1,1}$-extension domain.
In this paper the necessary and sufficient conditions were given for Orlicz-Lorentz function space endowed with the Orlicz norm having non-squareness and local uniform non-squareness.
We prove thatthe Banach space $(oplus_{n=1}^infty ell_p^n)_{ell_q}$, which is isomorphic to certain Besov spaces, has a greedy basis whenever $1leq p leqinfty$ and $1<q<infty$. Furthermore, the Banach spaces $(oplus_{n=1}^infty ell_p^n)_{ell_1}$, wit