Pointwise convergence approximate identities of dilated radially decreasing kernels

Author:
R. A. Kerman

Journal:
Proc. Amer. Math. Soc. **101** (1987), 41-44

MSC:
Primary 42B99; Secondary 44A35

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897067-7

MathSciNet review:
897067

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Abstract: Let be integrable on with . It is shown that

**[1]**A. P. Calderon and A. Zygmund,*On the existence of certain singular integrals*, Acta Math.**88**(1952), 85–139. MR**0052553**, https://doi.org/10.1007/BF02392130**[2]**G. H. Hardy,*Further researches in the theory of divergent series and integrals*, Proc. Cambridge Philos. Soc.**21**(1908), 1-48.**[3]**-,*Fourier's double integral and the theory of divergent integrals*, Proc. Cambridge Philos. Soc.**21**(1911), 427-451.**[4]**-,*Notes on some points in the integral calculus*(XLII):*On Weierstrass's singular integral and on a theorem of Lerch*, Messenger Math.**46**(1917), 43-48.**[5]**I. I. Hirschman and D. V. Widder,*The convolution transform*, Princeton University Press, Princeton, N. J., 1955. MR**0073746****[6]**E. C. Titchmarsh,*Theory of Fourier integrals*, 2nd ed., Oxford Univ. Press, 1962.

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0897067-7

Article copyright:
© Copyright 1987
American Mathematical Society