Júlio S. Neves

University of Coimbra | UC · Department of Mathematics

The aim of the paper is to establish (local) optimal embeddings of Besov spaces Bp,r0,b involving only a slowly varying smoothness b. In general, our target spaces are outside of the scale of Lorentz–Karamata spaces. In particular, we improve results from Caetano (2011), where the targets are (local) Lorentz–Karamata spaces. To derive such results,...

The aim of the paper is to establish (local) optimal embeddings of Besov spaces $B^{0,b}_{p,r}$ involving only a slowly varying smoothness $b$. In general, our target spaces are outside of the scale of Lorentz-Karamata spaces and are related to small Lebesgue spaces. In particular, we improve results from [CGO11b], where the targets are (local) Lor...

We study traces on the boundary of generalized smoothness Morrey spaces on Ck domains Ω. These spaces are equipped with three parameters s,p,q and a function parameter φ. Our results remain valid for the usual Besov–Morrey spaces Nu,p,qs(Ω), Triebel–Lizorkin–Morrey spaces Eu,p,qs(Ω), and Triebel–Lizorkin type spaces Fp,qs,τ(Ω), which are all includ...

Let ρ be a monotone quasinorm defined on ${\rm {\frak M}}^ + $ , the set of all non-negative measurable functions on [0, ∞). Let T be a monotone quasilinear operator on ${\rm {\frak M}}^ + $ . We show that the following inequality restricted on the cone of λ -quasiconcave functions $$\rho (Tf) \les C_1\left( {\int_0^\infty {f^p} v} \right)^{1/p},$$...

We study traces on the boundary of generalized smoothness Morrey spaces on C k domains Ω. These spaces are equipped with three parameters s, p, q and a function parameter ϕ. Our results remain valid for the usual Besov-Morrey spaces N s u,p,q (Ω), Triebel-Lizorkin-Morrey spaces E s u,p,q (Ω), and Triebel-Lizorkin type spaces F s,τ p,q (Ω), which ar...

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a Lp-Lebesgue space, of a function f in WkL[Formula presented],p(Ω), where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, k,n∈N, k<n and [Formula presented]<p<+∞. This sharp estimate is used to establish necessary and sufficient conditions for contin...

In this work we propose a novel method for identifying individuals based on retinal fundus image matching. The method is based on the image registration of retina blood vessels, since it is known that the retina vasculature of an individual is a signature, i.e., a distinctive pattern of the individual. The proposed image registration consists of a...

We study traces in 2-microlocal Triebel-Lizorkin spaces with variable integrability F-p(.)(,q(.))w(R-n) on hyperplanes using atomic decompositions. Our results cover spaces of variable smoothness and variable integrability and also weighted spaces studied extensively in recent years. We also study the trace of Besov spaces B-p(.)(,q)w(R-n) and Trie...

Retinal fundus images are widely used for screening, diagnosis and prognosis purposes in ophthalmology. Additionally these can also be used in retinal identification/recognition systems, for identification/authentication of an identity. In this paper the aim is to explain how norms in function spaces can be used to set up, automatically, classes of...

We study necessary and sufficient conditions for embeddings of Besov spaces of generalized smoothness Bp,qσ,N(Rn) into generalized Hölder spaces Λ∞,rμ(⋅)(Rn) when s¯(Nτ−1)>0 and τ−1∈ℓq′, where τ=σN−n/p. A borderline situation, corresponding to the limiting situation in the classical case, is included and give new results. In particular, we characte...

We use an estimate of the k-modulus of smoothness of a function f such that the norm of its distributional gradient |∇ k f | belongs locally to the Lorentz space L n/k,1 (R n), k ∈ N, k ≤ n, and we prove its reverse form to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces. These spaces are modelled upon...

We study traces in 2-microlocal Besov spaces with variable integrability on hyperplanes using atomic decompositions. Our results cover spaces of variable smoothness and also weighted spaces studied extensively in recent years.

We establish necessary and sufficient conditions for embeddings of Bessel potential spaces H σ X(IR n ) with order of smoothness σ ∈ (0, n), modelled upon rearrangement invariant Banach function spaces X(IR n ), into generalized Hölder spaces (involving k-modulus of smoothness). We apply our results to the case when X(IR n ) is the Lorentz-Karama...

We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), respectively, into generalized Hölder spaces L¥,rm()( \mathbb Rn)\Lambda_{\infty,r}^{\mu(\cdot)}(\e...

We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces H σ X(R n), modelled upon a rearrangement--invariant Banach function spaces X(R n), into generalized Hölder spaces involving k-modulus of smoothness. To this end, we derive a characterization of compact subsets of generalized Hölder spaces. We...

Let X(ℝn) = X(ℝn, μn) be a rearrangement-invariant Banach function space over the measure space (ℝn, μn), where μn stands for the n-dimensional Lebesgue measure in ℝn. We derive a sharp estimate for the k-modulus of smoothness of the convolution of a function f ∈ X(ℝn) with the Bessel potential kernel gσ, where σ ∈ (0, n). Such an estimate states t...

The continuity envelope for the Besov and Triebel-Lizorkin spaces of generalized smoothness B pq (s,Ψ)(ℝn ) and F pq (s,Ψ)(ℝn ), respectively, are computed in the critical case s=n/p, provided that Ψ satisfies an appropriate critical condition. Surprisingly, in this critical situation, the corresponding optimal index is ∞, when compared with all th...

First, we establish necessary and sufficient conditions for embeddings of Bessel potential spaces HsX(\mathbb Rn){H^{\sigma}X(\mathbb R^n)} with order of smoothness less than one, modelled upon rearrangement invariant Banach function spaces X(\mathbb Rn){X(\mathbb R^n)}, into generalized Hölder spaces. To this end, we derive a sharp estimate of...

The present paper is devoted to the study of growth envelopes of anisotropic function spaces. An affirmative answer is given to the question of H. Triebel [Wavelet bases in anisotropic function spaces. In: Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA-04). Praha: Math. Inst. Acad. Czech Rep. 2005, pp. 370-387; Conjecture 13...

We establish embeddings for Bessel potential spaces modeled upon Lorentz–Karamata spaces with order of smoothness less than one. The target spaces are of Hölder-continuous type. In the super-limiting case we also prove that the embedding is sharp and fails to be compact. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Sharpness and non-compactness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces are pre- sented. Target spaces are Lorentz-Karamata spaces and generalised Holder spaces. As consequences of these results, growth and continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces are ob- tai...

We establish the sharpness of embedding theorems for Bessel- potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Holder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata...

We establish sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz–Karamata (LK) spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are LK spaces. As a consequence of our results, we get growth envelopes of Bessel-potential spaces modelled upon LK spaces.

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We consider Bessel-potential spaces modelled upon Lorentz-Karamata spaces and establish embedding theorems in the super-limiting case. In addition, we refine a result due to Triebel, in the context of Bessel-potential spaces, itself an improvement of the Brézis-Wainger result (super-limiting case) about the “almost Lipschitz continuity” of elements...

We consider Lorentz-Karamata spaces and establish embedding theorems (some local and some global) for Bessel-potential spaces modelled upon appropriate Lorentz-Karamata spaces into Lorentz-Karamata spaces and Orlicz spaces. In particular, we obtain refinements of the Sobolev embedding theorems: Strichartz-Trudinger's limiting case and Hansson-Brézi...

General Besov -Hölder-Lipschitz spaces (ℝn ), where ρ is an arbitrary q-admissible function, are introduced and extrapolation characterizations concerning these spaces are given. We present some concrete examples and, in particular, we very easily obtain the extrapolation results [16, Proposition 2.5], [8, Proposition 4.2] and [14, Proposition 7]....