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1.
The continuity envelope for the Besov and Triebel-Lizorkin spaces of generalized smoothness B pq (s,Ψ)(ℝ n ) and F pq (s,Ψ)(ℝ n ), 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 the known results. Moreover, in the particular case of the classical spaces, we solve an open problem posed by Haroske in Envelopes and Sharp Embeddings of Function Spaces, Research Notes in Mathematics, vol. 437, Chapman & Hall, Boca Raton, 2007. As an immediate application of our results we give an upper estimate for approximation numbers of related embeddings.  相似文献   

2.
Given a metric space with a Borel measure, we consider the classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function summable with some power. We prove embedding theorems for these spaces defined by two different measures satisfying the doubling condition.  相似文献   

3.
We prove a sharp version of the endpoint Sobolev embedding in the context of non-linear function classes with mixed norms.  相似文献   

4.
Besov  O. V. 《Mathematical Notes》2019,106(3-4):501-513
Mathematical Notes - We establish an embedding theorem for spaces of functions of positive smoothness defined on irregular domains of n-dimensional Euclidean space in spaces of the same type and...  相似文献   

5.
Doklady Mathematics - For spaces of functions of positive smoothness defined on irregular domains of n-dimensional Euclidean space, an embedding theorem into spaces of the same type is proved and...  相似文献   

6.
For weighted spaces of functions of positive smoothness on irregular domains, embedding theorems into weighted Lebesgue spaces are proved.  相似文献   

7.
8.
We improve the Sobolev-type embeddings due to Gagliardo (Ric Mat 7:102–137, 1958) and Nirenberg (Ann Sc Norm Sup Pisa 13:115–162, 1959) in the setting of rearrangement invariant (r.i.) spaces. In particular, we concentrate on seeking the optimal domains and the optimal ranges for these embeddings between r.i. spaces and mixed norm spaces. As a consequence, we prove that the classical estimate for the standard Sobolev space \(W^{1}L^{p}\) by Poornima (Bull Sci Math 107(3):253–259,  1983), O’Neil (Duke Math J 30:129–142,  1963) and Peetre (Ann Inst Fourier 16(1):279–317,  1966) (\(1 \le p < n\)), and by Hansson (Math Scand 45(1):77–102,  1979, Brezis and Wainger (Commun Partial Differ Equ 5(7):773–789,  1980) and Maz’ya (Sobolev spaces,  1985) (\(p=n\)) can be further strengthened by considering mixed norms on the target spaces.  相似文献   

9.
The concept of local growth envelope of the quasi-normed function space is applied to the Triebel-Lizorkin spaces of generalized smoothness In order to achieve this, a standardization result for these and corresponding Besov spaces is derived.  相似文献   

10.
Mikulevičius  R.  Phonsom  C. 《Potential Analysis》2019,50(3):467-519
Potential Analysis - Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and...  相似文献   

11.
Let 1 < p < , 0 < v < p', let be a bounded domainin Rn, and denote by id the limiting compact embedding of theBesov space (Rn) into the exponentialOrlicz space Lexp(tv)(), mapping a function f onto its restrictionf|. In 1993 Triebel established, among others, two-sided estimatesfor the entropy numbers of id, which are even asymptoticallyoptimal for ‘small’ . The aim of the paper is toimprove the upper bounds in the case of ‘large’, where Triebel's estimates are not yet sharp, thus making afurther step towards the conjectured correct asymptotic behaviour.  相似文献   

12.
We review in these notes the theory of equivariant embeddings of spherical homogeneous spaces. Given a spherical homogeneous space G/H, the normal equivariant embeddings of G/H are classified by combinatorial objects called colored fans, which generalize the fans appearing in the classification of toric varieties and which encode several geometric properties of the corresponding variety.  相似文献   

13.
14.
It is well known that there are bounded domains Rn whose boundaries are not smooth enough for there to exist a bounded linear extensionfor the Sobolev space into , but the embedding is nevertheless compact. For the Lipboundaries (0<<1) studied in [3, 4], there does not existin general an extension operator of into but there is a bounded linear extension of into and the smoothness retained by thisextension is enough to ensure that the embedding is compact. It is natural to ask if this is typicalfor bounded domains which are such that is compact, that is, that there exists a boundedextension into a space of functions in Rn which enjoy adequatesmoothness. This is the question which originally motivatedthis paper. Specifically we study the ‘extension by zero’operator on a space of functions with given ‘generalized’smoothness defined on a domain with an irregular boundary, anddetermine the target space with respect to which it is bounded.  相似文献   

15.
In this article,the authors first establish the pointwise characterizations of Besov and Triebel-Lizorkin spaces with generalized smoothness on Rn via the Haj?a...  相似文献   

16.
Using the relation between the set of embeddings of tori into Euclidean spaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new results on embeddings of tori into Euclidean spaces.  相似文献   

17.
Compactness of embeddings between rearrangement invariant spaces is closely related to absolute continuity of these embeddings. We study absolutely continuous embeddings between rearrangement invariant spaces. In particular it is shown that an absolutely continuous embedding is never optimal. We give sufficient (and under additional hypotheses necessary) conditions for absolute continuity of these embeddings. We also provide quantitative estimates of absolutely continuous embeddings.  相似文献   

18.
A Banach space E of measurable functions on [0,1] is called rearrangement invariant if E is a Banach lattice and equimeasurable functions have identical norms. The canonical inclusion E ? F of two rearrangement invariant spaces is said to be strict if functions from the unit ball of E have absolutely equicontinuous norms in F. Necessary and sufficient conditions for the strictness of canonical inclusion for Orlicz, Lorentz, and Marcinkiewicz spaces are obtained, and the relations of this concept to the disjoint strict singularity are studied.  相似文献   

19.
Let be a non-degenerate polar space of rank n 3 where all of its lines have at least three points. We prove that, if admits a lax embedding e : in a projective space defined over a skewfield K, then is a classical and defined over a sub-skewfield K0 of K. Accordingly, admits a full embedding e0 in a K0-projective space 0. We also prove that, under suitable hypotheses on e and e0, there exists an embedding such that and preserves dimensions.Received: March, 2004  相似文献   

20.
Given a metric measure space X, we consider a scale of function spaces \(T^{p,q}_s(X)\), called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on X we identify some associated interpolation spaces, in particular certain real interpolation spaces. These are identified with a new scale of function spaces, which we call Z -spaces, that have recently appeared in the work of Barton and Mayboroda on elliptic boundary value problems with boundary data in Besov spaces. We also prove Hardy–Littlewood–Sobolev-type embeddings between weighted tent spaces.  相似文献   

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