Abstract
In this paper, the boundedness of Toeplitz operator T b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε \(\dot \Lambda _{\beta _0 } \) (ℝn) is discussed from L p(ℝn) to L q(ℝn), \(\tfrac{1}{q} = \tfrac{1}{p} - \tfrac{{\beta _0 }}{n}\), and from L p(ℝn) to Triebel-Lizorkin space \(\dot F_p^{\beta _0 ,\infty } \). We also obtain the boundedness of generalized Toeplitz operator Θ b α0 from L p(ℝn) to L q(ℝn), \(\tfrac{1}{q} = \tfrac{1}{p} - \tfrac{{\alpha _0 + \beta _0 }}{n}\). All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator T b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L p(ℝn), 1 < p < ∞.
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Lin, Y., Lu, S. Toeplitz operators related to strongly singular Calderón-Zygmund operators. SCI CHINA SER A 49, 1048–1064 (2006). https://doi.org/10.1007/s11425-006-1084-7
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DOI: https://doi.org/10.1007/s11425-006-1084-7