Results 21 to 23 of about 23 (23)

On a measure of non‐compactness for singular integrals

Journal of Function Spaces, Volume 1, Issue 1, Page 35-43, 2003., 2003
It is proved that there exists no weight pair (v, w) for which a singular integral operator is compact from the weighted Lebesgue space Lwp(Rn) to Lvp(Rn). Moreover, a measure of non‐compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.
Alexander Meskhi
wiley   +1 more source

Singular integrals and potentials in some Banach function spaces with variable exponent

Journal of Function Spaces, Volume 1, Issue 1, Page 45-59, 2003., 2003
We introduce a new Banach function space ‐ a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponent p(t) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ω(t) = |t|β is related
Vakhtang Kokilashvili, Stefan Samko
wiley   +1 more source

Charaterisation of function spaces via mollification; fractal quantities for distributions

Journal of Function Spaces, Volume 1, Issue 1, Page 75-89, 2003., 2003
The aim of this paper is twofold. First we characterise elements f belonging to the Besov spaces Bpqs(ℝn) with s ∈ ℝ, 0 < p ≤ ∞, 0 < q ≤ ∞, in terms of their mollifications. Secondly we use these results to study multifractal quantities for distributions generalising well‐known corresponding quantities for Radon measures.
Hans Triebel
wiley   +1 more source