Integral, Differential and Multiplication Operators on Generalized Fock Spaces

摘要

Volterra companion integral and multiplication operators with holomorphic symbols are studied for a large class of generalized Fock spaces on the complex plane C. The weights defining these spaces are radial and subject to a mild smoothness condition. In addition, we assumed that the weights decay faster than the classical Gaussian weight. One of our main results show that there exists no nontrivial holomorphic symbols g which induce bounded Volterra companion integral Ig and multiplication operators Mg acting between the weighted spaces. We also describe the bounded and compact Volterra-type integral operators Vg acting between Fq and Fp when at least one of the exponents p or q is infinite, and extend results of Constantin and Pelaez for finite exponent cases. Furthermore, we showed that the differential operator D acts in unbounded fashion on these and the classical Fock spaces.