论文标题
可变lebesgue空间上的ε-最大运算符和HAAR乘数
The ε-Maximal Operator and Haar Multipliers on Variable Lebesgue Spaces
论文作者
论文摘要
C. Stockdale，P。Villarroya和B. Wick介绍了$ε$ - 毫米运算符，以证明HAAR乘数在加权空间$ l^p（w）$上，用于大于$ a_p $的一类。我们证明$ε$ -maximal运算符和HAAR乘数在可变的Lebesgue Spaces $ \ lpp（\ r^n）$上限制在更大的指数函数中，而不是使用log-holder连续功能，用于证明最大运算符在$ \ lpp（\ r^n）上的最大操作员的界限。我们还证明，当仅限于二元立方体$ q_0 $时，HAAR乘数是紧凑的。
C. Stockdale, P. Villarroya, and B. Wick introduced the $ε$-maximal operator to prove the Haar multiplier is bounded on the weighted spaces $L^p(w)$ for a class of weights larger than $A_p$. We prove the $ε$-maximal operator and Haar multiplier are bounded on variable Lebesgue spaces $\Lpp(\R^n)$ for a larger collection of exponent functions than the log-Holder continuous functions used to prove the boundedness of the maximal operator on $\Lpp(\R^n)$. We also prove that the Haar multiplier is compact when restricted to a dyadic cube $Q_0$.
