Besov spaces with non-doubling measures
Besov spaces with non-doubling measures
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DOI：
10.1090/s0002-9947-05-03787-6
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发表时间：
2005-06
影响因子：
1.3
通讯作者：
D. Deng;Yongsheng Han;Dachun Yang
中科院分区：
文献类型：
--
作者：
D. Deng;Yongsheng Han;Dachun Yang
假设μ是Rd上的Radon测度，它可以是非加倍的。μ的唯一条件是增长条件，即存在一个常数C0> 0使得对所有x ∈ supp（μ）和r > 0，μ（B（x，r））≤ C0 rn，其中0 0是依赖于非倍测度μ，C0，n和d的真实的数.用于定义这些空间的方法是新的，即使是经典的情况。作为应用，利用Riesz位势算子和对偶空间得到了这些空间的提升性质。
Suppose that μ is a Radon measure on R d , which may be non-doubling. The only condition on μ is the growth condition, namely, there is a constant C 0 > 0 such that for all x ∈ supp (μ) and r > 0, μ(B(x,r)) ≤ C 0 r n , where 0 0 is a real number which depends on the non-doubling measure μ, C 0 , n and d. The method used to define these spaces is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are obtained.