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Integral operators with rough kernels in variable Lebesgue spaces
Acta Mathematica Hungarica ( IF 0.9 ) Pub Date : 2020-05-19 , DOI: 10.1007/s10474-020-01045-2 M. Urciuolo , L. Vallejos
Acta Mathematica Hungarica ( IF 0.9 ) Pub Date : 2020-05-19 , DOI: 10.1007/s10474-020-01045-2 M. Urciuolo , L. Vallejos
We study integral operators with kernels $$K(x,y)= k_{1}( x- A_1y) \cdots k_{m}( x-A_my),$$ K ( x , y ) = k 1 ( x - A 1 y ) ⋯ k m ( x - A m y ) , $$k_{i}(x)=\frac{\Omega_{i}(x)}{|x|^{n/q_i}}$$ k i ( x ) = Ω i ( x ) | x | n / q i where $$\Omega_{i} \colon \mathbb{R}^{n} \to \mathbb{R}$$ Ω i : R n → R are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and $$\frac n{q_1}+\cdots+ \frac n{q_m} = n - \alpha, 0 \leq \alpha
中文翻译：
可变 Lebesgue 空间中具有粗糙核的积分算子
我们研究带有内核的积分运算符 $$K(x,y)= k_{1}( x- A_1y) \cdots k_{m}( x-A_my),$$ K ( x , y ) = k 1 ( x - A 1 y ) ⋯ km ( x - A my ) , $$k_{i}(x)=\frac{\Omega_{i}(x)}{|x|^{n/q_i}}$$ ki ( x ) = Ω i ( x ) | × | n / qi 其中 $$\Omega_{i} \colon \mathbb{R}^{n} \to \mathbb{R}$$ Ω i : R n → R 是零次齐次函数，满足大小和Dini 条件，A i 是某些可逆矩阵，$$\frac n{q_1}+\cdots+ \frac n{q_m} = n - \alpha, 0 \leq \alpha
更新日期：2020-05-19
中文翻译：
可变 Lebesgue 空间中具有粗糙核的积分算子
我们研究带有内核的积分运算符 $$K(x,y)= k_{1}( x- A_1y) \cdots k_{m}( x-A_my),$$ K ( x , y ) = k 1 ( x - A 1 y ) ⋯ km ( x - A my ) , $$k_{i}(x)=\frac{\Omega_{i}(x)}{|x|^{n/q_i}}$$ ki ( x ) = Ω i ( x ) | × | n / qi 其中 $$\Omega_{i} \colon \mathbb{R}^{n} \to \mathbb{R}$$ Ω i : R n → R 是零次齐次函数，满足大小和Dini 条件，A i 是某些可逆矩阵，$$\frac n{q_1}+\cdots+ \frac n{q_m} = n - \alpha, 0 \leq \alpha
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