Results 11 to 19 of about 19 (19)
Quantitative functional calculus in Sobolev spaces
Journal of Function Spaces, Volume 2, Issue 3, Page 279-321, 2004., 2004 In the frame work of Sobolev (Bessel potential) spaces Hn(Rd, R or C), we consider the nonlinear Nemytskij operator sending a function x ∈ Rd ↦ f(x) into a composite function x ∈ Rd ↦ G(f(x), x). Assuming sufficient smoothness for G, we give a “tame” bound on the Hn norm of this composite function in terms of a linear function of the Hn norm of f, with
Carlo Morosi +2 more
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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
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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
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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
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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
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Estimates for convolutions in the anisotropic Nikol′skiĭ‐Besov spaces
Journal of Function Spaces, Volume 1, Issue 1, Page 91-106, 2003., 2003 We obtain various estimates for convolutions in the anisotropic Nikol′skiĭ‐Besov spaces of functions of several real variables possessing some common smoothness of, in general, fractional order which may be different with respect to different variables.
V. I. Burenkov, G. E. García Almeida
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On a class of nonclassical hyperbolic equations with nonlocal conditions
International Journal of Stochastic Analysis, Volume 15, Issue 2, Page 125-140, 2002., 2002 This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract ...
Abdelfatah Bouziani
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International Journal of Stochastic Analysis, Volume 15, Issue 3, Page 207-219, 2002., 2002 In this paper we are concerned with the heteroscedastic regression model yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi, ti, ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β.
Han-Ying Liang, Bing-Yi Jing
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Oscillation criteria for a class of partial functional‐differential equations of higher order
International Journal of Stochastic Analysis, Volume 15, Issue 3, Page 255-267, 2002., 2002 Higher order partial differential equations with functional arguments including hyperbolic equations and beam equations are studied. Sufficient conditions are derived for every solution of certain boundary value problems to be oscillatory in a cylindrical domain.
Tariel Kiguradze +2 more
wiley +1 more source