Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T08:15:22.607Z Has data issue: false hasContentIssue false

On approximation properties of the parabolic potentials

Published online by Cambridge University Press:  17 April 2009

Simten B. Uyhan
Affiliation:
Department of Mathematics, Akdeniz University, Antalya, Turkey, e-mail: [email protected]
A.D. Gadjiev
Affiliation:
Department of Mathematics, Akdeniz University, Antalya, Turkey, e-mail: [email protected]
Ilham A. Aliev
Affiliation:
Institute of Math. and Mech., National Academy of Sciences, Azerbaijan Baku, Turkey, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper the approximation properties of parabolic potentials Hαf and ℋαf generated by the heat operators and , where

are studied as α → 0+.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Aliev, I.A. and Rubin, B., ‘Parabolic wavelet transforms and Lebesque spaces of parabolic potentials’, Rocky Mountain J. Math. 32 (2002), 391408.CrossRefGoogle Scholar
[2]Aliev, I.A. and Rubin, B., ‘Parabolic potentials and wavelet transforms with the generalized translation’, Studia Math. 145 (2001), 116.CrossRefGoogle Scholar
[3]Bagby, R., ‘Lebesque spaces of parabolic potentials’, Illinois J. Math. 15 (1971), 610634.CrossRefGoogle Scholar
[4]Chanillo, S., ‘Hypersingular integrals and parabolic potentials’, Trans. Amer. Math. Soc. 267 (1981), 531547.CrossRefGoogle Scholar
[5]Gadjiev, A.D. and Aliev, I.A., ‘On a class of potentials type operators generated by the generalized translation’, (in Russian), Reports of the I.N. Vekua Inst. Appl. Math. (Tbilisi) 3 (1988), 2124.Google Scholar
[6]Rao, V.R. Gopala, ‘A characterization of parabolic functions spaces’, Amer. J. Math. 99 (1977), 985993.CrossRefGoogle Scholar
[7]Jones, B.F., ‘Lipschitz spaces and heat equation’, J. Math. Mech. 18 (1968), 379410.Google Scholar
[8]Kurokawa, T., ‘On the Riesz and Bessel kernels as approximations of the identity’, Sci. Rep. Kagoshima Univ. 30 (1981), 3145.Google Scholar
[9]Nogin, V.A. and Rubin, B.S., ‘The spaces of parabolic potentials’, Anal. Math. 13 (1987), 321338.Google Scholar
[10]Samko, S.G., Kilbas, A.A. and Marichev, O.I., Fractional integrals and derivatives: Theory and applications (Gordon and Breach, New York, 1993).Google Scholar
[11]Sampson, C.H., A characterization of parabolic Lebesque spaces, (Ph.D. Dissertation) (Rice University, Houston, TX., 1968).Google Scholar
[12]Stein, E. and Weiss, G., ‘Introduction to Fourier analysis on Euclidean spaces’ (Princeton Uni v. Press, Princeton, N.J.).Google Scholar