Results 11 to 20 of about 22 (22)

A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

open access: yesJournal of Function Spaces, Volume 2, Issue 1, Page 55-69, 2004., 2004
A trace inequality for the generalized Riesz potentials Iα(x) is established in spaces Lp(x) defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two‐weighted inequality in classical Lebesgue spaces for potentials Iα(x) defined on fractal sets is derived.
David E. Edmunds   +3 more
wiley   +1 more source

The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems

open access: yesJournal of Function Spaces, Volume 2, Issue 1, Page 71-95, 2004., 2004
In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that
George Isac   +2 more
wiley   +1 more source

Note on the paper “Regulated domains and Bergman type projections”

open access: yesJournal of Function Spaces, Volume 2, Issue 2, Page 97-106, 2004., 2004
We show that the sufficient condition of the above mentioned paper is also necessary for the boundedness of Bergman type projections on a class of regulated domains.
Jari Taskinen, Miroslav Englis
wiley   +1 more source

Pseudodifferential operators on α‐modulation spaces

open access: yesJournal 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
wiley   +1 more source

Local uniform convexity and Kadec‐Klee type properties in K‐interpolation spaces I: General Theory

open access: yesJournal 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
wiley   +1 more source

The Hadamard‐Schwarz inequality

open access: yesJournal 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
wiley   +1 more source

Quantitative functional calculus in Sobolev spaces

open access: yesJournal 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
wiley   +1 more source

Local Uniform Convexity and Kadec‐Klee Type Properties in K‐interpolation spaces II

open access: yesJournal 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

open access: yesJournal 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

open access: yesJournal 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
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