Quantitative Weighted Estimates of the L q -Type Rough Singular Integral Operator and Its Commutator

Shuo Wang (), Peize Lv and Xiangxing Tao
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Shuo Wang: Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China
Peize Lv: Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China
Xiangxing Tao: Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China

Mathematics, 2025, vol. 13, issue 21, 1-19

Abstract: Let Ω be a homogeneous function of degree zero on R n , n ≥ 2 , integrable and having mean value zero on the unit sphere S n − 1 , and let T Ω 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 A 1 − A ∞ weighted estimates for T Ω under the rough condition Ω ∈ L q ( S n − 1 ) for some q ∈ ( 1 , ∞ ) . The results of the paper improve the previous works for the case Ω ∈ L ∞ ( S n − 1 ) . We also give the quantitative A 1 − A ∞ weighted estimates for the commutator [ b , T Ω ] with B M O symbol b .

Keywords: quantitative weighted estimate; commutator; singular integral; rough kernel of L q type (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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