As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with error estimate n−1 log n, provided one of the generators has a bounded H∞ functional calculus.
We establish a Fredholm criterion for the operators belonging to the C∗-algebra generated by singular integral operators with semi-almost periodic matrix coefficients.
In Section 5, we obtain compactness criteria for the operators defined by (1) and (2).
In Section 3, we recall the definition, history and some essential properties of amalgam spaces with a constant exponent, and also known results about the boundedness of some integral operators in these spaces; boundedness criteria for the operators K v and K v in VEAS are also established.
The additional edge set (mathcal {E}_{c_{1}(s),c_{2}(s)}) is chosen such that (mathcal {G}_{s}) is an induced subgraph, which as mentioned above is the desired criterion for the merging operator.
We have offered a criterion for the composition operator with closed range on, but it seems that it is difficult to check whether or not satisfies the -reverse Carleson measure condition.
positive measurable function on [ a, b ), − ∞ < a < b ≤ ∞, and let ( H v, w ( a, b ) f ) ( x ) = v ( x ) ∫ a x f ( t ) w ( t ) d t, x ∈ [ a, b ). Further, we denote. Let us recall the two-weight criterion for the Hardy operator in classical Lebesgue spaces: Theorem A ([27, 28]).
Now we formulate the boundedness criteria for the kernel operator ( K v f ) = v ( x ) ∫ − ∞ x k ( x, t ) f ( t ) d t, x ∈ R, on amalgams defined on ℝ.
