Abstract:
We study the action of composition operators on Sobolev spaces
of analytic functions in some weighted Bergman and Hardy spaces on the
unit disc. Composition operators mapping into the Hardy space are
included by making particular choices for the weights.
We show the construction of the translating of certain classical
inequalities for Hardy spaces to inequalities for Bergman spaces and then
how to translate them to special inequalities for Hardy spaces , moreover
we prove a relation of the equality on the general Lebesgue space and
calculate a recognizable estimate for the exterma of the best possible
constant.
We show that Hardy space be contained in the Bergman space
when they are equivalent to Hilbert space by finding the multipliers of
Hardy space into Bergman spaces in the unit disc and show a
generalization of pointwise multipliers from weighted Bergman spaces
and Hardy to weighted Bergman spaces.
