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MULTIPLIER THEOREMS IN WEIGHTED SMIRNOV SPACES

  • Guven, Ali (DEPARTMENT OF MATHEMATICS FACULTY OF ART AND SCIENCE BALIKESIR UNIVERSITY) ;
  • Israfilov, Daniyal M. (DEPARTMENT OF MATHEMATICS FACULTY OF ART AND SCIENCE BALIKESIR UNIVERSITY)
  • Published : 2008.11.01

Abstract

The analogues of Marcinkiewicz multiplier theorem and Littlewood-Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.

Keywords

References

  1. A. Bottcher and Yu I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, Progress in Mathematics, 154. Birkhauser Verlag, Basel, 1997
  2. G. David, Operateurs integraux singuliers sur certaines courbes du plan complexe, Ann. Sci. Ecole Norm. Sup. (4) 17 (1984), no. 1, 157-189 https://doi.org/10.24033/asens.1469
  3. P. L. Duren, Theory of $H^{p}$ Spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London, 1970
  4. G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Translation of Mathematical Monographs, Vol.26, Providence, RI, 1969
  5. D. M. Israfilov, Approximation by p-Faber polynomials in the weighted Smirnov class $E^{p}$(G, $\omega$) and the Bieberbach polynomials, Constr. Approx. 17 (2001), no. 3, 335-351 https://doi.org/10.1007/s003650010030
  6. D. M. Israfilov, Approximation by p-Faber-Laurent rational functions in the weighted Lebesgue spaces, Czechoslovak Math. J. 54(129) (2004), no. 3, 751-765 https://doi.org/10.1007/s10587-004-6423-7
  7. D. M. Israfilov and A. Guven, Approximation in weighted Smirnov classes, East J. Approx. 11 (2005), no. 1, 91-102
  8. V. Kokilashvili, A direct theorem for the approximation in the mean of analytic functions by polynomials, Dokl. Akad. Nauk SSSR 185 (1969), 749-752
  9. D. S. Kurtz, Littlewood-Paley and multiplier theorems on weighted $L^{p}$ spaces, Trans. Amer. Math. Soc. 259 (1980), no. 1, 235-254 https://doi.org/10.2307/1998156
  10. J. E. Littlewood and R. Paley, Theorems on Fourier series and power series, Proc. London Math. Soc. 42 (1936), 52-89 https://doi.org/10.1112/plms/s2-42.1.52
  11. J. Marcinkiewicz, Sur les Multiplicateurs des Series de Fourier, Studia Math. 8 (1939), 78-91 https://doi.org/10.4064/sm-8-1-78-91
  12. B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226 https://doi.org/10.2307/1995882
  13. P. K. Suetin, Series of Faber Polynomials, Gordon and Breach Science Publishers, Amsterdam, 1998
  14. M. F. Timan, Inverse theorems of the constructive theory of functions in $L_{p}$ spaces $(1\leq{p}\leq \infty)$, Mat. Sb. N.S. 46(88) (1958), 125-132
  15. M. F. Timan, On Jackson's theorem in $L_{p}$-spaces, Ukrain. Mat. Z. 18 (1966), no. 1, 134-137 https://doi.org/10.1007/BF02537726
  16. A. Zygmund, Trigonometric Series, Vol. I-II, Cambridge Univ. Press, 2nd edition, 1959