Structure of weighted Hardy spaces on finitely connected domains
We give a complete characterization of a certain class of Hardy type spaces on finitely connected planar domains. In particular, we provide a decomposition result and give a description of such functions through their boundary values. As an application, we describe an isomorphism from the weighted Hardy space onto the classical Hardy-Smirnov space. This allows us to identify the multiplier space of the mentioned Hardy type spaces as the space of bounded holomorphic functions on the domain.******************************************************************************************
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- [1] M.A. Alan, Hardy spaces on hyperconvex domains, M.Sc. Thesis, Middle East Technical
University, Ankara, 2003.
- [2] M.A. Alan and N.G. Göğüş, Poletsky-Stessin-Hardy spaces in the plane, Complex
Anal. Oper. Theory, 8 (5), 975–990, 2014.
- [3] B. Chevreau, C.M. Pearcy and A.L. Shields, Finitely connected domains $G$, representations
of $H^{\infty}(G)$, and invariant subspaces, J. Operator Theory, 6, 375–405, 1981.
- [4] J.P. Demailly, Mesure de Monge Ampère et mesures plurisousharmonique, Math. Z.
194, 519–564, 1987.
- [5] P.L. Duren, Theory of $H^p$ spaces, Pure and Applied Mathematics 38, Academic Press,
New York-London, 1970.
- [6] N. G. Göğüş, Structure of weighted Hardy spaces in the plane, Filomat, 30 (2),
473–482, 2016.
- [7] S. Krantz, Geometric function theory. Explorations in complex analysis, Cornerstones,
Birkhäuser Boston, Inc., Boston, MA, 2006.
- [8] E.A. Poletsky and K. Shrestha, On weighted Hardy spaces on the unit disk, Constructive
approximation of functions, 195–204, Banach Center Publ. 107, Polish Acad.
Sci. Inst. Math., Warsaw, 2015.
- [9] E.A. Poletsky and M.I. Stessin, Hardy and Bergman spaces on hyperconvex domains
and their composition operators, Indiana Univ. Math. J. 57 (5), 2153–2201, 2008.
- [10] D. Sarason, Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture
Notes in the Mathematical Sciences, 10, John Wiley and Sons, Inc., New York, 1994.
- [11] K.R. Shrestha, Weighted Hardy spaces on the unit disk, Complex Anal. Oper. Theory,
9 (6), 1377–1389, 2015.
- [12] S. Şahin, Poletsky-Stessin Hardy spaces on domains bounded by an analytic Jordan
curve in C, Complex Var. Elliptic Equ. 60 (8), 1114–1132, 2015.