Browse > Article
http://dx.doi.org/10.4134/JKMS.2008.45.6.1535

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)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.6, 2008 , pp. 1535-1548 More about this Journal
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
Carleson curve; p-Faber polynomials; Muckenhoupt weight; weighted Smirnov space;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 G. David, Operateurs integraux singuliers sur certaines courbes du plan complexe, Ann. Sci. Ecole Norm. Sup. (4) 17 (1984), no. 1, 157-189   DOI
2 A. Bottcher and Yu I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators, Progress in Mathematics, 154. Birkhauser Verlag, Basel, 1997
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   DOI
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   DOI
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 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
10 M. F. Timan, On Jackson's theorem in $L_{p}$-spaces, Ukrain. Mat. Z. 18 (1966), no. 1, 134-137   DOI
11 A. Zygmund, Trigonometric Series, Vol. I-II, Cambridge Univ. Press, 2nd edition, 1959
12 B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226   DOI   ScienceOn
13 D. S. Kurtz, Littlewood-Paley and multiplier theorems on weighted $L^{p}$ spaces, Trans. Amer. Math. Soc. 259 (1980), no. 1, 235-254   DOI
14 J. E. Littlewood and R. Paley, Theorems on Fourier series and power series, Proc. London Math. Soc. 42 (1936), 52-89   DOI
15 J. Marcinkiewicz, Sur les Multiplicateurs des Series de Fourier, Studia Math. 8 (1939), 78-91   DOI
16 P. K. Suetin, Series of Faber Polynomials, Gordon and Breach Science Publishers, Amsterdam, 1998