Results 21 to 25 of about 25 (25)
Local Uniform Convexity and Kadec‐Klee Type Properties in K‐interpolation spaces II
Journal of Function Spaces, Volume 2, Issue 3, Page 323-356, 2004., 2004 We study local uniform convexity and Kadec‐Klee type properties in K‐interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non‐commutative Lorentz spaces possess the (so‐alled) (DGL)‐property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous ...
Peter G. Dodds +4 more
wiley +1 more source
Hardy operator with variable limits on monotone functions
Journal of Function Spaces, Volume 1, Issue 1, Page 1-15, 2003., 2003 We characterize weighted Lp − Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non‐negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits.
Vladimir D. Stepanov, Elena P. Ushakova
wiley +1 more source
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