Let G denote a locally compact Hausdorff abelian group. Then a bounded linear operator T from L^2(G) into L^2(G) is a bounded multiplier operator if, under the Fourier transform on L^2(G ), for each function f in L^2(G), T(f) changes into a bounded function U times the Fourier transform of f. Then U is called the multiplier of T. An unbounded multiplier operator has a similar definition, but it...

We study finite delay evolution equation { x′(t) = Ax(t) + F (t, xt), t ≥ 0, x0 = φ ∈ C ([−r, 0] , E) , where linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First we obtain some properties of “integral solutions” in this case, and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn’s fixed point theorem to prove...

It is well known that the Hilbert tranformation and the conjugate function operator restricted to even (odd) functions define bounded linear operators on weighted If spaces under more general conditions than is the case for the unrestricted operators. In analogy with recent results of Hunt, Muckenhoupt and Wheeden for the Hilbert transform and the conjugate function operator, we obtain necessar...

The paper is devoted to an invertible linear operator whose inverse is a Hilbert Schmidt operator and imaginary Hermitian component is bounded. Numerous regular differential and integro-differential operators satisfy these conditions. A sharp norm estimate for the resolvent of the considered operator is established. It gives us estimates for the semigroup and so-called Hirsch operator functions...

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Let T be a bounded linear, or sublinear, operator from L p (Y) to L q (X). To any sequence of subsets Y j of Y is associated a maximal operator T f(x) = sup j jT (f Yj)(x)j. Under the hypotheses that q > p and the sets Y j are nested, we prove that T is also bounded. Classical theorems of Menshov and Zygmund are obtained as corollaries. Multilinear generalizations of this theorem are also estab...

We study the intertwining relation XTφ = TψX where Tφ and Tψ are the Toeplitz operators induced on the Hardy space H 2 by analytic functions φ and ψ, bounded on the open unit disc U, and X is a nonzero bounded linear operator on H. Our work centers on the connection between intertwining and the image containment ψ(U) ⊂ φ(U), as well as on the nature of the intertwining operator X. We use our re...

The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L p (ν) (0 < p < r < ∞) which satisfies a vector-valued norm inequality