A new class of Hardy spaces in the plane

Year 2017, Volume: 46 Issue: 4, 559 - 565, 01.08.2017

Muhammed Ali Alan Nihat Gökhan Göğüş

Abstract

We introduce new spaces that are extensions of the Hardy spaces and prove a removable singularity result for holomorphic functions within these spaces. Additionally we provide non-trivial examples.

Keywords

Hardy space, Removable singularity

References

• Alan, M. A. and Gö§ü³, N. G. Poletsky-Stessin-Hardy spaces in the plane, Complex Anal. Oper. Theory 8 (2014), no. 5, 975990.
• Demailly, J. P. Mesure de Monge-Ampère et mesures plurisousharmonique, Math. Z. 194 (1987), 519564.
• Duren, P. L. Theory of Hp spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London 1970.
• Göğüş, N. G. Structure of weighted Hardy spaces in the plane, Filomat 30, (2016) no. 2, 473-482.
• Jarnicki, P. and Pug, P. Extension of Holomorphic Functions, De Gruyter Expositions in Mathematics 34
• Järvi, P. Removable singularities for Hp-functions, Proc. Amer. Math. Soc. 86 (1982), 596 598.
• Lelong, P. Fonctions plurisousharmoniques et formes dierentielles positives, Gordon and Breach, New York, 1968.
• Parreau, M. Sur les moyennes des fonctions harmoniques et analytiques et la classication des surfaces de Riemann, Ann. Inst. Fourier (Grenoble) 3 (1951), 103197.
• Poletsky, E. A. and Stessin, M. I. Hardy and Bergman spaces on hyperconvex domains and their composition operators, Indiana Univ. Math. J. 57 (2008), no. 5, 21532201.
• Şahin, S., Poletsky-Stessin Hardy spaces on domains bounded by an analytic Jordan curve in C, Complex Var. Elliptic Equ. 60 (2015), no. 8, 11141132
• Shrestha, K. R. Weighted Hardy spaces on the unit disk, Complex Anal. Oper. Theory 9 (2015), no. 6, 13771389.