参数型Littlewood-Paley算子在带非双倍测度Morrey空间上的有界性(英文)

Boundedness of Parametrized Littlewood-Paley Operators with Non-doubling Measures on Morrey Spaces

假定μ是仅满足一个增长条件的Radon测度,即存在一个正常数C使得对所有的x∈Rd,r>0以及对某个固定的n∈(0,d]都成立μ(B(x,r))≤Crn.对适当的参数ρ和λ,证明了参数型g*λ函数M*,ρλ和参数型Marcinkiewicz积分Mρ在Morrey空间Mp q(k,μ)上是有界的.

Let μ be a non-negative Radon measure on R^d which only satisfies the following growth condition that there exists a positive constant C such that μ（B（x,r））≤Cr^n for all x∈R^d, r〉0 and some fixed n∈（0,d]. We will prove that for suitable indexesρandλthe parametrized gλ^＊function Mλ^＊ ρand Mρare bounded on M q^p （k, μ） spaces.