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We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol $g$ on the Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^p$. We showed that $V_g$ is bounded on $\mathcal{F}_{\psi_m}^p$ if and only if $g$ is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of $g$ being not bigger than one. We also identified all those positive numbers $p$ for which the operator $V_g$ belongs to the Schatten $\mathcal{S}_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of $g$.
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참고문헌 (24)
참고문헌 신청
A. Aleman / 1995 / An integral operator on Hp / Complex Variables Theory Appl 28 (2) : 149 ~ 158
A. Aleman / 1997 / Integration operators on Bergman spaces / Indiana University Math J 46 (2) : 337 ~ 356
A. Aleman / 2001 / An integral operator on Hp and Hardy's inequality / J. Anal. Math 85 : 157 ~ 176
A. Schuster / 2012 / Teoplitz operators and Carleson measures on generalized Bergmann-Fock spaces / Integr. Equ. Oper. Theory 72 : 363 ~ 392
D. Girela / 2006 / Carleson measures, multipliers and integration operators for spaces of Dirichlet type / J. Funct. Anal 241 (1) : 334 ~ 358
A. Aleman / 1997 / Integration operators on Bergman spaces / Indiana University Math J 46 (2) : 337 ~ 356
A. Aleman / 2001 / An integral operator on Hp and Hardy's inequality / J. Anal. Math 85 : 157 ~ 176
A. Schuster / 2012 / Teoplitz operators and Carleson measures on generalized Bergmann-Fock spaces / Integr. Equ. Oper. Theory 72 : 363 ~ 392
D. Girela / 2006 / Carleson measures, multipliers and integration operators for spaces of Dirichlet type / J. Funct. Anal 241 (1) : 334 ~ 358
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