Abstract:
We give remarks on the construction of linear
evolution
equations.
Logarithms
and
some
examples
of
unbounded imaginary powers of operators are considered, and
we determined the best constants in Young's inequality and its
converse with its generalization to more than three functions.
We show a hypercontractivity for multipliers on the orthogonal
polynomials and estimates for oscillatory integrals and their
extended domains. We studied the boundedness of oscillatory
singular
integrals
on
Lebesgue
and
Hardy
spaces.
We
established the differentiability of fractional powers of self-
adjoint operators. We show some applications of the purely
imaginary powers of operators in Hilbert spaces. We present
the Contractivity of the free semigroups and singular operators
on Boson fields as forms on spaces of entire functions on
Hilbert spaces with uniform estimates for oscillatory integral
.operators
