Quantitative Weighted Estimates of the Lq-Type Rough Singular Integral Operator and Its Commutator
Year: 2025
Type: article
Abstract: Let Ω be a homogeneous function of degree zero on Rn, n≥2, integrable and having mean value zero on the unit sphere Sn−1, and let TΩ be the homogeneous convolution singular integral operator with kernel Ω(x)|x|n. By introducing reasonable refined decomposition and approximation techniques, together with sparse domination and variable measure interpolation methods, we establish the quantitative A1−A∞ weighted estimates for TΩ under the rough condition Ω∈Lq(Sn−1) for some q∈(1,∞). The results of the paper improve the previous works for the case Ω∈L∞(Sn−1). We also give the quantitative A1−A∞ weighted estimates for the commutator [b,TΩ] with BMO symbol b.
Source: Mathematics
DOI: 10.3390/math13213434
Authors: Shuo Wang, Peize Lv, Xiangxing Tao
Institution: Zhejiang University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Award: G3885376140
OpenAlex ID: W4415625396