Essential norms of integral operators
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We estimate the essential norms of Volterra-type integral operators $ V_g$ and $ I_g$, and multiplication operators $M_g$ with holomorphic symbols $g$ on a large class of generalized Fock spaces on the complex plane $\mathbb {C}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol $g$ and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.
Abstract
We estimate the essential norms of Volterra-type integral operators $ V_g$ and $ I_g$, and multiplication operators $M_g$ with holomorphic symbols $g$ on a large class of generalized Fock spaces on the complex plane $\mathbb {C}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol $g$ and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.
참고문헌 (22)
- A. Aleman, "Topics in complex analysis and operator theory", pp.3~30 (2007), Univ. Malaga
- B. J. Carswell, "Composition operators on the Fock space", Acta Sci. Math. (Szeged), 69(3-4), pp.871~887 (2003)
- S. Chandrasekhar, "Radiative Transfer" (1950), Oxford University Press
- O. Constantin, "A Volterra-type integration operator on Fock spaces", Proc. Amer. Math. Soc, 140(12), pp.4247~4257 (2012)
- O. Constantin, "Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces", J. Geom. Anal, 26(2), pp.1109~1154 (2016)
- C. Corduneanu, "Integral Equations and Applications" (1991), Cambridge University Press
- Z. Cuckovic, "Weighted composition operators on the Bergman space", J. London Math. Soc, 70(2), pp.499~511 (2004)
- Z. Cuckovic, "Weighted composition operators between different weighted Bergman spaces and different Hardy spaces", Illinois J. Math, 51(2), pp.479~498 (2007)
- K. Deimling, "Nonlinear Functional Analysis" (1985), Springer-Verlag
- S. Hu, "Integral equations arising in the kinetic theory of gases", Appl. Anal, 34(3-4), pp.261~266 (1989)
- S. Janson, "Hankel forms and the Fock space", Rev. Mat. Iberoamericana, 3(1), pp.61~138 (1987)
- T. Mengestie, "Volterra type and weighted composition operators on weighted Fock spaces", Integral Equations Operator Theory, 76(1), pp.81~94 (2013)
- T. Mengestie, "Product of Volterra type integral and composition operators on weighted Fock spaces", J. Geom. Anal, 24(2), pp.740~755 (2014)
- T. Mengestie, "Carleson type measures for Fock-Sobolev spaces", Complex Anal. Oper. Theory, 8(6), pp.1225~1256 (2014)
- Tesfa Mengestie, "Integral, Differential and Multiplication Operators on Generalized Fock Spaces", Complex Analysis and Operator Theory, 13(3), pp.935~958 (2019), Springer Science and Business Media LLC[DOI]
- D. O'Regan, "Existence Theory for Nonlinear Integral and Integrodiffer-ential Equations" (1998), Kluwer Academic Publishers
- J. Pau, "Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights", J. Funct. Anal, 259(10), pp.2727~2756 (2010)
- J. Rattya, "The essential norm of a composition operator mapping into the Qs-space", J. Math. Anal. Appl, 333(2), pp.787~797 (2007)
- J. H. Shapiro, "The essential norm of a composition operator", Ann. of Math, 125(2), pp.375~404 (1987)
- A. G. Siskakis, "Volterra operators on spaces of analytic functions|a survey", Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, pp.51~68 (2006), Univ. Sevilla Secr. Publ
- S. Stevic, "Weighted composition operators between Fock-type spaces in CN", Appl. Math. Comput, 215(7), pp.2750~2760 (2009)
- S.-I. Ueki, "Weighted composition operators on some function spaces of entire functions", Bull. Belg. Math. Soc. Simon Stevin, 17(2), pp.343~353 (2010)