Abstract
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.
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References
K K Chen. Theory of Trigonometric Series, Iwanami Shoten, Tokyo, 1930.
I Daubechies. Ten Lecture on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol 61, SIAM, Philadephia, 1992.
L Grafakos. Classical and Modern Fourier Analysis, Pearson Education, New Jersey, 2004.
K W Li, W C Sun. Pointwise convergence of the Calderon reproducing formula, J Fourier Anal Appl, 2012, 18(3): 439–455.
M A Pinsky. Introduction to Fourier analysis and wavelets, Brooks Cole, Pacific Grove, 2002.
X L Shi, J Sun. Pointwise convergence of inverse wavelet transforms, Preprint.
F Weisz. Summability of Multi-Dimensional Fourier Series and Hardy Spaces, Mathematics and Its Applications, Vol 541, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
F Weisz. Inversion formulas for the continuous wavelet transform, Acta Math Hungar, 2013, 138(3): 237–258.
A Zygmund. Trigonometric Series, 3rd ed, Cambridge University Press, London, 2002.
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Hu, L., Shi, Xl. Pointwise convergence of some conjugate convolution operators with applications to wavelets. Appl. Math. J. Chin. Univ. 31, 320–330 (2016). https://doi.org/10.1007/s11766-016-3418-8
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DOI: https://doi.org/10.1007/s11766-016-3418-8