Results 21 to 30 of about 61 (61)
Pseudodifferential operators on α‐modulation spaces
Journal of Function Spaces, Volume 2, Issue 2, Page 107-123, 2004., 2004 We study expansions of pseudodifferential operators from the Hörmander class in a special family of functions called brushlets. We prove that such operators have a sparse representation in a brushlet system. Using this sparsity, we show that a pseudodifferential operator extends to a bounded operator between α‐modulation spaces.
Lasse Borup, Richard Rochberg
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Local uniform convexity and Kadec‐Klee type properties in K‐interpolation spaces I: General Theory
Journal of Function Spaces, Volume 2, Issue 2, Page 125-173, 2004., 2004 We present a systematic study of the interpolation of local uniform convexity and Kadec‐Klee type properties in K‐interpolation spaces. Using properties of the K‐functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K‐interpolation functional which guarantee that a given K ...
Peter G. Dodds +4 more
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The Hadamard‐Schwarz inequality
Journal of Function Spaces, Volume 2, Issue 2, Page 191-215, 2004., 2004 Given α1, …, αk arbitrary exterior forms in Rn of degree l1, …, lk, does it follow that |α1∧⋯∧αk| ≤ |α1| ⋯ |αk| The answer is no in general. However, it is a persistent, popular and even published misconception that the answer is yes. Of course, a routine calculation reveals that there exists at least a constant Cn independent of the forms satisfying ...
Tadeusz Iwaniec +4 more
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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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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
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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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