A Note on the Paper "Hermitian Operators on C(X, E) and Banach-Stone Theorem" by R.J. Fleming and J.E.Jamison.
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 problem of linear conjugation for analytic functions with boundary values from the Zygmund class.
A remark on Fefferman-Stein's inequalities.
It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
A remark on symbols of an operator
A remark on the asymmetry of convolution operators
A convolution operator, bounded on , is bounded on , with the same operator norm, if and are conjugate exponents. It is well known that this fact is false if we replace with a general non-commutative locally compact group . In this paper we give a simple construction of a convolution operator on a suitable compact group , wich is bounded on for every and is unbounded on if .
A sharp rearrangement inequality for the fractional maximal operator
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
A simple proof of the continuity of the higher order Riesz transforms with respect to the gaussian measure
A study of some constants characterizing the weighted Hardy inequality
A version of the Grothendieck theorem for subspaces of analytic functions in lattices.
A weighted estimate for an intermediate operator on the cone of nonnegative functions.
A₁-regularity and boundedness of Calderón-Zygmund operators
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...
Absolutely continuous linear operators on Köthe-Bochner spaces
Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let and be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.
Algebraic and essentially algebraic composition operators on C(X).
Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals.
Almost regular operators and integral operators on rearrangement invariant p-spaces of functions,
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
An Example of Quantum Exponential Process.
An extension of the theory of Fredholm determinants