具有非卷积型核的多线性Littlewood-Paley算子在Campanato空间上的新估计

New estimates for multilinear Littlewood-Paley operators with non-convolution type kernels on Campanato spaces

考虑具有非卷积型核的多线性Littlewood-Paley算子在Campanato空间上的有界性,其中包括多线性g-函数,多线性Lusin面积积分S和多线性g_λ*-函数.证明了如果f=(f_1,…,f_n),f_i∈ε^(α_i,p_i)(R^n),i=1,…,m,那么g(f),S(f),g_λ*(f)几乎处处等于无穷或几乎处处有限,且在后一种情形下,算子[g(f)]~2,[S(f)]~2,[g_λ*(f)]~2从ε^(α_1,p_1)(R^n)×…×ε^(α_m,p_m)(R^n)到ε_*^(2_(α,p)/2)(R^n)是有界的.

This paper considers the boundedness of multilinear Littlewood-Paley operators with non-convolution type on Campanato spaces,including the multilinear g function,multilinear Lusin's area integral S and multilinear g*λ-function.If f=(f1,…,fn),fi∈εαi,pi(Rn),i=1,…,m,then g(f),S(f),g*λ(f)are either infinite everywhere or finite almost everywhere,and in the latter case,[g(f)]2,[S(f)]2,[g*λ(f)]2are bounded fromεα1,p1(Rn)×…×εαm,pm(Rn)toε2α,p/2*(Rn).