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Multiplier theorems in weighted Smirnov spaces

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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.

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.

참고문헌 (16)

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  3. P. L. Duren, "Theory of Hp Spaces, Pure and Applied Mathematics, Vol. 38" (1970), Academic Press
  4. G. M. Goluzin, "Geometric Theory of Functions of a Complex Variable, Translation of Mathematical Monographs, Vol.26" (1969), Providence
  5. D. M. Israfilov, "Approximation by p-Faber polynomials in the weighted Smirnov class Ep(G, ω) and the Bieberbach polynomials", Constructive Approximation, 17(3), pp.335~351 (2001)
  6. D. M. Israfilov, "Approximation by p-Faber-Laurent rational functions in the weighted Lebesgue spaces", CZECHOSLOVAK MATHEMATICAL JOURNAL, 54(3), pp.751~765 (2004)
  7. D. M. Israfilov, "Approximation in weighted Smirnov classes", East Journal on Approximations, 11(1), pp.91~102 (2005)
  8. V. Kokilaˇshvili, "A direct theorem for the approximation in the mean of analytic functions by polynomials", Doklady Akademii Nauk SSSR, 185, pp.74~952
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  10. J. E. Littlewood, "Theorems on Fourier series and power series", Proceedings of the London Mathematical Society, 통권 : 42, pp.52~89 (1936)
  11. J. Marcinkiewicz, "Sur les Multiplicateurs des Series de Fourier", Studia Mathematica, 8, pp.78~91 (1939)
  12. B. Muckenhoupt, "Weighted norm inequalities for the Hardy maximal function", Transactions of the American Mathematical Society, 165, pp.207~226 (1972)
  13. P. K. Suetin, "Series of Faber Polynomials" (1998), Gordon and Breach Science Publishers
  14. M. F. Timan, "Inverse theorems of the constructive theory of functions in Lp spaces (1 ≤ p ≤ ∞)", mathematics of the USSR-Sbornik (N.S.), 46, pp.125~132 (1958)
  15. M. F. Timan, "On Jackson’s theorem in Lp-spaces", Ukrainian Mathematical Journal, 18(1), pp.134~137 (1966)
  16. A. Zygmund, "Trigonometric Series, Vol. I-II" (1959), Cambridge Univ. Press

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