Weighted Herz Spaces and Regularity Results - Yuxing Guo; Yinsheng Jiang (Journal of Function Spaces and Applications)
It is proved that, for the nondivergence form elliptic equations ∑𝑛𝑖,𝑗=1𝑎𝑖𝑗𝑢𝑥𝑖𝑥𝑗=𝑓, if 𝑓 belongs to the weighted Herz spaces 𝐾𝑞𝑝(𝜑,𝑤), then 𝑢𝑥𝑖𝑥𝑗∈𝐾𝑞𝑝(𝜑,𝑤), where 𝑢 is the 𝑊2,𝑝-solution of the equations. In order to obtain this, the authors first establish the weighted boundedness for the commutators of some singular integral operators on 𝐾𝑞𝑝(𝜑,𝑤).