COMPOSITION OPERATORS BETWEEN HARDY AND BLOCH-TYPE SPACES OF THE UPPER HALF-PLANE

Title & Authors
COMPOSITION OPERATORS BETWEEN HARDY AND BLOCH-TYPE SPACES OF THE UPPER HALF-PLANE
Sharma, S.D.; Sharma, Ajay K.; Ahmed, Shabir;

Abstract
In this paper, we study composition operators $\small{C_{\varph}f=f^{\circ}{\varph}}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.
Keywords
composition operator;Bloch-type spaces;Hardy spaces;
Language
English
Cited by
1.
On a product-type operator from weighted Bergman–Orlicz space to some weighted type spaces, Applied Mathematics and Computation, 2015, 256, 37
2.
Weighted composition operators between Hardy and growth spaces on the upper half-plane, Applied Mathematics and Computation, 2011, 217, 10, 4928
3.
Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces, Applied Mathematics and Computation, 2015, 268, 966
4.
Composition operators from the weighted Bergman space to the nth weighted-type space on the upper half-plane, Applied Mathematics and Computation, 2010, 217, 7, 3379
5.
Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane, Abstract and Applied Analysis, 2009, 2009, 1
6.
Composition operators from the Hardy space to the nth weighted-type space on the unit disk and the half-plane, Applied Mathematics and Computation, 2010, 215, 11, 3950
7.
Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane, Abstract and Applied Analysis, 2011, 2011, 1
8.
Compact Composition Operators on the Bloch Space and the Growth Space of the Upper Half-Plane, Mediterranean Journal of Mathematics, 2017, 14, 2
References
1.
P. L. Duren, Theory of \$H^p\$ spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London, 1970

2.
K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962

3.
J. E. Littlewood, On inequalities in the theory of functions, Proc. Lond. Math. Soc. (2) 23 (1925), 481-519

4.
V. Matache, Composition operators on \$H^p\$ of the upper half-plane, An. Univ. Timisoara Ser. Stiint. Mat. 27 (1989), no. 1, 63-66

5.
V. Matache, Composition operators on Hardy spaces of a half-plane, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1483-1491

6.
S. Ohno and R. Zhao, Weighted composition operators on the Bloch space, Bull. Austral. Math. Soc. 63 (2001), no. 2, 177-185

7.
S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215

8.
W. Rudin, Real and complex analysis, Third edition. McGraw-Hill Book Co., New York, 1987

9.
S. D. Sharma, Compact and Hilbert-Schmidt composition operators on Hardy spaces of the upper half-plane, Acta Sci. Math. (Szeged) 46 (1983), no. 1-4, 197-202

10.
S. D. Sharma, A. K. Sharma, and S. Ahmed, Carleson measures in a vector-valued Bergman space, J. Anal. Appl. 4 (2006), no. 1, 65-76

11.
R. K. Singh, A relation between composition operators on \$H^2(D)\$ and \$H^2(P^+)\$, Pure Appl. Math. Sci. 1 (1974/75), no. 2, 1-5

12.
R. K. Singh and S. D. Sharma, Composition operators on a functional Hilbert space, Bull. Austral. Math. Soc. 20 (1979), no. 3, 377-384

13.
R. K. Singh and S. D. Sharma, Noncompact composition operators, Bull. Austral. Math. Soc. 21 (1980), no. 1, 125-130