Results 1 to 10 of about 19 (19)
Journal of Function Spaces, Volume 3, Issue 1, Page 33-71, 2005., 2005 Continuity envelopes for the spaces of generalised smoothness Bpq(s,Ψ)(ℝn) and Fpq(s,Ψ)(ℝn) are studied in the so‐called supercritical s = 1 + n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings
António M. Caetano +2 more
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Journal of Function Spaces, Volume 3, Issue 1, Page 73-89, 2005., 2005 We consider a generalized version of the small Lebesgue spaces, introduced in [5] as the associate spaces of the grand Lebesgue spaces. We find a simplified expression for the norm, prove relevant properties, compute the fundamental function and discuss the comparison with the Orlicz spaces.
Claudia Capone +2 more
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Traces of multipliers in pairs of weighted Sobolev spaces
Journal of Function Spaces, Volume 3, Issue 1, Page 91-115, 2005., 2005 We prove that the pointwise multipliers acting in a pair of fractional Sobolev spaces form the space of boundary traces of multipliers in a pair of weighted Sobolev space of functions in a domain.
Vladimir Maz′ya +2 more
wiley +1 more source
Spaces of complex functions and vector measures in incomplete spaces
Journal of Function Spaces, Volume 2, Issue 1, Page 1-16, 2004., 2004 It is known that the space L1(μ) of complex functions which are integrable with respect to a vector measure μ taking values in a (not neessarily complete) locally convex space is not an ideal, in general. We discuss several natural properties which L1(μ) may or may not possess and consider various implications between these properties. For a particular
Werner Riker +2 more
wiley +1 more source
Spaces of Test Functions via the STFT
Journal of Function Spaces, Volume 2, Issue 1, Page 25-53, 2004., 2004 We characterize several classes of test functions, among them Björck′s ultra‐rapidly decaying test functions and the Gelfand‐Shilov spaces of type S, in terms of the decay of their short‐time Fourier transform and in terms of their Gabor coefficients.
Karlheinz Gröchenig +2 more
wiley +1 more source
A trace inequality for generalized potentials in Lebesgue spaces with variable exponent
Journal 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
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Note on the paper “Regulated domains and Bergman type projections”
Journal 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
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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
wiley +1 more source