Hu, Lan; Shi, Xianliang Pointwise convergence of some conjugate convolution operators with applications to wavelets. (English) Zbl 1374.42013 Appl. Math., Ser. B (Engl. Ed.) 31, No. 3, 320-330 (2016). Summary: In this paper, we discuss the pointwise convergence of conjugate convolution operators with some applications to wavelets. Some criteria of convergence at \((C, 1)\) continuous points, Lebesgue points and almost everywhere are established. MSC: 42A50 Conjugate functions, conjugate series, singular integrals 42A85 Convolution, factorization for one variable harmonic analysis Keywords:Hilbert transform; pointwise convergence; wavelet PDFBibTeX XMLCite \textit{L. Hu} and \textit{X. Shi}, Appl. Math., Ser. B (Engl. Ed.) 31, No. 3, 320--330 (2016; Zbl 1374.42013) Full Text: DOI References: [1] K K Chen. Theory of Trigonometric Series, Iwanami Shoten, Tokyo, 1930. [2] I Daubechies. Ten Lecture on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol 61, SIAM, Philadephia, 1992. · Zbl 0776.42018 [3] L Grafakos. Classical and Modern Fourier Analysis, Pearson Education, New Jersey, 2004. · Zbl 1148.42001 [4] K W Li, W C Sun. Pointwise convergence of the Calderon reproducing formula, J Fourier Anal Appl, 2012, 18(3): 439–455. · Zbl 1250.42095 · doi:10.1007/s00041-011-9211-4 [5] M A Pinsky. Introduction to Fourier analysis and wavelets, Brooks Cole, Pacific Grove, 2002. · Zbl 1065.42001 [6] X L Shi, J Sun. Pointwise convergence of inverse wavelet transforms, Preprint. [7] F Weisz. Summability of Multi-Dimensional Fourier Series and Hardy Spaces, Mathematics and Its Applications, Vol 541, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002. · Zbl 1306.42003 [8] F Weisz. Inversion formulas for the continuous wavelet transform, Acta Math Hungar, 2013, 138(3): 237–258. · Zbl 1289.42096 · doi:10.1007/s10474-012-0263-y [9] A Zygmund. Trigonometric Series, 3rd ed, Cambridge University Press, London, 2002. · Zbl 1084.42003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.