A commutator theorem for fractional integrals in spaces of homogeneous type.
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A function-theoretic proof of a theorem of Stampfli
A Hilbert-type linear operator with the norm and its applications.
A new Hilbert-type linear operator with a composite kernel and its applications.
A note on extreme contractions on -spaces
A note on matrix transformations of holomorphic Dirichlet series.
A note on strictly cyclic shifts on .
A note on the powers of Cesàro bounded operators
In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies
A remark concerning Putinar's model of hyponormal weighted shifts
The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
A remark on extrapolation of rearrangement operators on dyadic , 0 < s ≤ 1
For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator , 0 < s < 2, to be the linear extension of the map , where denotes the -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that is bounded on , then for all 0 < s < 2 the operator is bounded on .
A remark on (p, q)-absolutely summing operators in -spaces
A remark on the multipliers on spaces of Weak Products of functions
If H denotes a Hilbert space of analytic functions on a region Ω ⊆ Cd , then the weak product is defined by [...] We prove that if H is a first order holomorphic Besov Hilbert space on the unit ball of Cd , then the multiplier algebras of H and of H ⊙ H coincide.
A singular functional-differential equation.
A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform
Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform and also all weighted dyadic martingale transforms are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.
A universal non-compact operator
Absolute and Ordinary Köthe-Toeplitz Duals of Some Sets of Sequences and Matrix Transformations
Absolutely Summing Terraced Matrices
Let α > 0. By Cα we mean the terraced matrix defined by [...] if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be [...] in the region 1/p + 1/q ≤ 1.
An abstract approach to some spectral problems of direct sum differential operators.
An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure
We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include...