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.
[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.
Year 2020,
Volume: 49 Issue: 4, 1450 - 1457, 06.08.2020
[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.
Göğüş, N. G. (2020). Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics, 49(4), 1450-1457. https://doi.org/10.15672/hujms.598004
AMA
Göğüş NG. Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics. August 2020;49(4):1450-1457. doi:10.15672/hujms.598004
Chicago
Göğüş, Nihat Gökhan. “Structure of Weighted Hardy Spaces on Finitely Connected Domains”. Hacettepe Journal of Mathematics and Statistics 49, no. 4 (August 2020): 1450-57. https://doi.org/10.15672/hujms.598004.
EndNote
Göğüş NG (August 1, 2020) Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics 49 4 1450–1457.
IEEE
N. G. Göğüş, “Structure of weighted Hardy spaces on finitely connected domains”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1450–1457, 2020, doi: 10.15672/hujms.598004.
ISNAD
Göğüş, Nihat Gökhan. “Structure of Weighted Hardy Spaces on Finitely Connected Domains”. Hacettepe Journal of Mathematics and Statistics 49/4 (August 2020), 1450-1457. https://doi.org/10.15672/hujms.598004.
JAMA
Göğüş NG. Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics. 2020;49:1450–1457.
MLA
Göğüş, Nihat Gökhan. “Structure of Weighted Hardy Spaces on Finitely Connected Domains”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, 2020, pp. 1450-7, doi:10.15672/hujms.598004.
Vancouver
Göğüş NG. Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1450-7.