Counterexamples for classical operators on Lorentz-Zygmund spaces

Multiplication Operators on Generalized Lorentz-zygmund Spaces

The invertible, compact and Fredholm multiplication operators on generalized Lorentz-Zygmund (GLZ) spaces Lp,q;α, 1 < p ≤ ∞, 1 ≤ q ≤ ∞, α in the Euclidean space R, are characterized in this paper.

On the Boundedness of Classical Operators on Weighted Lorentz Spaces

Conditions on weights u(·), v(·) are given so that a classical operator T sends the weighted Lorentz space Lrs(vdx) into Lpq(udx). Here T is either a fractional maximal operator Mα or a fractional integral operator Iα or a Calderón–Zygmund operator. A characterization of this boundedness is obtained for Mα and Iα when the weights have some usual properties and max(r, s) ≤ min(p, q). § 0. Introd...

Volterra-Type Operators on Zygmund Spaces

Multilinear Calderón-zygmund Operators on Hardy Spaces

It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.

On Embeddings between Classical Lorentz Spaces

Let p 2 (0; 1), let v be a weight on (0; 1) and let p (v) be the classical Lorentz space, determined by the norm kfk p (v) := (R 1 0 (f (t)) p v(t) dt) 1=p. When p 2 (1; 1), this space is known to be a Banach space if and only if v is non-increasing, while it is only equivalent to a Banach space if and only if p (v) = ? p (v), where kfk ? p (v) := (R 1 0 (f (t)) p v(t) dt) 1=p. We may thus conc...