Herz型Besov空间的一些性质

Some Properties on Herz-type Besov Spaces

给出了Herz型Besov空间,Kα,pqBsβ(Rn)和 Kα,pqBsβ(Rn),一些基本性质:嵌入性质,极大不等式,Fourier乘子定理,提升性质,其中s∈R,0<β≤∞,0<q。

Some properties on the Herztype Besov spaces, Kα,pqBsβ(Rn)and α,pqBsβ(Rn),where s∈R,0<β≤∞,0<q,p<∞and -n/q<α were given. And some fundamental properties were also given: the embedding property, such as the Schwartz class is continuously embedded into the Herz type Besov spaces;the maximal function inequality; the Fourier multiplier Theorem; the lifting property, that means Iσ maps Kα,pqBsβ(Rn) isomorphically onto Kα,pqBs-σβ(Rn) and ‖Iσf‖Kα,pqBs-σβ is an equivalent quasinorm on Kα,pqBsβ(Rn), where, Iσf=F-1(1+|x|2)σ/2Ff, and Ff is the Fourier transform of function f and F-1 is the inverse Fourier transform.