Abstract
Abstract Let 𝑚 ∈ 𝑛 and 𝑎1, . . . , 𝑎𝑚 be real numbers such that for each 𝑖, 𝑎𝑖 ≠ 0 and 𝑎𝑖 ≠ 𝑎𝑗 if 𝑖 ≠ 𝑗. In this paper we study integral operators of the form 𝑇𝑓 (𝑥) = ∫ 𝑘1 (𝑥 – 𝑎1𝑦) . . . 𝑘𝑚 (𝑥 – 𝑎𝑚𝑦) 𝑓 (𝑦) 𝑑𝑦, with . If φ 𝑖,𝑗 satisfy certain uniform regularity conditions out of the origin, we obtain the boundedness of 𝑇 : 𝐿𝑝(𝑤) → 𝐿𝑝(𝑤) for all power weights 𝑤 in adequate Muckenhoupt classes.
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