Interpolation of Rational Approximation Spaces Belonging to the Besov Class
- 44 Downloads
The Peetre real interpolation method is realized for the Besov class of spaces of analytic functions on the circle. We obtain a description of interpolation norms with the help of difference-differential constructions. We consider rational approximation spaces in the BMOA and H p norms.
Key wordsrational approximation space analytic function Besov space interpolation norm BMO space BMOA norm Hp norm
Unable to display preview. Download preview PDF.
- 1.V. V. Peller, “Hankel operators of class σp and their applications (rational approximation, Gaussian processes, problem of majorization of operators),” Mat. Sb. [tMath. USSR-Sb.], 113 (1980), no. 4, 538–581.Google Scholar
- 2.V. V. Peller, “The description of Hankel operators of class σp for p > 0, the study of the rate of rational approximation and other applications,” Mat. Sb. [Math. USSR-Sb.], 122 (1983), no. 4, 481–510.Google Scholar
- 3.A. A. Pekarskii, “The classes of analytic functions-defined by best approximations in H p” Mat. Sb. [Math. USSR-Sb.], 127 (1985), no. 1, 3–39.Google Scholar
- 4.A. A. Pekarskii, “Chebyshev rational approximations in the disk, on the circle, and on the closed interval,” Mat. Sb. [Math. USSR-Sb.], 133 (1987), no. 1, 86–102.Google Scholar
- 5.Yu. V. Netrusov, “Interpolation (real-variable method) of spaces of smooth functions,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 325 (1992), no. 6, 1120–1123.Google Scholar
- 6.Yu. V. Netrusov, “Nonlinear approximation of functions from the Besov-Lorentz spaces in the uniform metric,” Zap. Nauchn. Sem. LOMI, 204 (1993), 61–81.Google Scholar
- 7.H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Birkhauser, Berlin, 1977.Google Scholar
- 8.J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-Heidelberg-New York, 1976.Google Scholar
- 9.V. L. Krepkogorskii, “Interpolation in Lizorkin-Triebel and Besov spaces,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 185 (1994), no. 7, 63–76.Google Scholar
- 10.P. Oswald, “On Besov-Hardy-Sobolev spaces of analytic functions in the unit disc,” Czechoslovak. Math. J., 33 (108) (1983), no. 3, 408–426.Google Scholar
- 11.D. Freitag, “Real interpolation of weighted L p-spaces,” Math. Nachr., 86 (1978), 15–18.Google Scholar