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1.
《Mathematische Nachrichten》2017,290(8-9):1177-1186
The aim of this paper is to establish the isomorphic classification of Besov spaces over [0, 1]d . Using the identification of the Besov space with the ‐infinite direct sum of finite‐dimensional spaces (which holds independently of the dimension and of the smoothness degree of the space ) we show that , , is a family of mutually non‐isomorphic spaces. The only exception is the isomorphism between the spaces and , which follows from Pełczyński's isomorphism between and . We also tell apart the isomorphic classes of spaces from the isomorphic classes of Besov spaces over the Euclidean space .  相似文献   

2.
《Mathematische Nachrichten》2017,290(5-6):852-866
Given non‐negative measurable functions on we study the high dimensional Hardy operator between Orlicz–Lorentz spaces , where f is a measurable function of and is the ball of radius t in . We give sufficient conditions of boundedness of and . We investigate also boundedness and compactness of between weighted and classical Lorentz spaces. The function spaces considered here do not need to be Banach spaces. Specifying the weights and the Orlicz functions we recover the existing results as well as we obtain new results in the new and old settings.  相似文献   

3.
《Mathematische Nachrichten》2018,291(1):109-127
We investigate how asymptotic properties of real sequences and are passed on to their tensor product . The main result concerns sequences of the form This problem is closely related to tensor stability of operator ideals on the Hilbert space.  相似文献   

4.
《Mathematische Nachrichten》2017,290(14-15):2111-2131
The paper deals with solutions of the Cauchy problem of a nonlinear generalized heat equation in the context of Besov and Triebel–Lizorkin spaces and where and with initial data belonging to some spaces where and .  相似文献   

5.
《Mathematische Nachrichten》2017,290(17-18):3038-3048
Let be the usual Besov spaces in bounded Lipschitz domains Ω in (bounded intervals if ). The paper clarifies under which conditions the continuous embedding between two such spaces with is nuclear.  相似文献   

6.
《Mathematische Nachrichten》2018,291(5-6):879-896
A J‐frame for a Krein space is in particular a frame for (in the Hilbert space sense). But it is also compatible with the indefinite inner‐product of , meaning that it determines a pair of maximal uniformly definite subspaces, an analogue to the maximal dual pair associated with an orthonormal basis in a Krein space. This work is devoted to study duality for J‐frames in Krein spaces. Also, tight and Parseval J‐frames are defined and characterized.  相似文献   

7.
《Mathematische Nachrichten》2017,290(17-18):2755-2758
A result showed by M. Gursky in 4 ensures that any metric g on the 4‐dimensional sphere satisfying and is isometric to the round metric. In this note, we prove that there exists a universal number i 0 such that any metric g on the 4‐dimensional sphere satisfying and is isometric to the round metric. Moreover, there exists a universal such that any metric g on the 4‐dimensional sphere with nonnegative sectional curvature, and is isometric to the round metric. This last result slightly improves a rigidity theorem also proved in 4 .  相似文献   

8.
《Mathematische Nachrichten》2017,290(16):2547-2559
We study the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces : they behave as if and as if . For we get the asymptotic behaviour up to a logarithmic factor.  相似文献   

9.
《Mathematische Nachrichten》2017,290(7):1066-1086
We consider embedding theorems within the scale of weighted Morrey spaces , where the weight w belongs to the Muckenhoupt class and . This includes, in particular, the classical setting of weighted Lebesgue spaces. We study some typical examples for the weight like , but also deal with quite general assumptions.  相似文献   

10.
《Mathematische Nachrichten》2017,290(11-12):1630-1636
We provide a generalization of the classical Schwarz theorem about the equality of mixed partial derivatives. More precisely we extend it to a Riemannian manifold , by proving the following statement: if is a couple of commuting vector fields on M and are such that the set is superdense at a certain point , then .  相似文献   

11.
《Mathematische Nachrichten》2018,291(11-12):1712-1726
We consider on the space polynomials that are invariant regarding permutations of the sequence variable or regarding finite permutations. Accordingly, they are trivial or factor through c0. The analogous study, with analogous results, is carried out on , replacing the permutations of by measurable bijections of that preserve the Lebesgue measure.  相似文献   

12.
《Mathematische Nachrichten》2017,290(5-6):930-954
As outlined below, this paper is devoted to a Carleson‐type‐measure‐based study of the holomorphic Campanato 2‐space on the open unit ball of , comprising all Hardy 2‐functions whose oscillations in non‐isotropic metric balls on the compact unit sphere are proportional to some power of the radius other than the dimension .  相似文献   

13.
《Mathematische Nachrichten》2018,291(5-6):759-773
We study the well‐posedness of the fractional degenerate differential equations with finite delay on Lebesgue–Bochner spaces , periodic Besov spaces and periodic Triebel–Lizorkin spaces , where A and M are closed linear operators on a Banach space X satisfying , F is a bounded linear operator from (resp. and ) into X, where is given by when and . Using known operator‐valued Fourier multiplier theorems, we give necessary or sufficient conditions for the well‐posedness of in the above three function spaces.  相似文献   

14.
《Mathematische Nachrichten》2017,290(5-6):726-737
In this paper, we study the well‐posedness of the degenerate differential equations with fractional derivative in Lebesgue–Bochner spaces , periodic Besov spaces and periodic Triebel–Lizorkin spaces , where A and M are closed linear operators in a complex Banach space X satisfying , and is the fractional derivative in the sense of Weyl. Using known operator‐valued Fourier multiplier results, we completely characterize the well‐posedness of this problem in the above three function spaces by the R‐bounedness (or the norm boundedness) of the M‐resolvent of A .  相似文献   

15.
《Mathematische Nachrichten》2018,291(11-12):1851-1858
We classify locally the contact metric ‐spaces whose Boeckx invariant is as tangent hyperquadric bundles of Lorentzian space forms.  相似文献   

16.
《Mathematische Nachrichten》2017,290(2-3):367-381
In this paper, we study the following Kirchhoff type elliptic problem with critical growth: where , and , and the nonlinear growth term reaches the Sobolev critical exponent since for four spatial dimensions. In a non‐radial symmetric function space, we establish a local compactness splitting lemma of critical version to investigate the existence of positive ground state solutions.  相似文献   

17.
We consider the generalized Anderson model , where is a countable set, are i.i.d. random variables and the are rank projections. For these models we prove theorem analogous to that of Jak?i?–Last on the equivalence of the trace measure for a.e. ω. Our model covers the dimer and polymer models.  相似文献   

18.
《Mathematische Nachrichten》2018,291(14-15):2318-2333
In this paper we study the zero‐flux chemotaxis‐system Ω being a convex smooth and bounded domain of , , and where , and . For any the chemotactic sensitivity function is assumed to behave as the prototype , with and . We prove that for nonnegative and sufficiently regular initial data and , the corresponding initial‐boundary value problem admits a unique globally bounded classical solution provided μ is large enough.  相似文献   

19.
Let M be a complete non‐compact Riemannian manifold satisfying the volume doubling property. Let be the Hodge–de Rham Laplacian acting on 1‐differential forms. According to the Bochner formula, where and are respectively the positive and negative part of the Ricci curvature and ? is the Levi–Civita connection. We study the boundedness of the Riesz transform from to and of the Riesz transform from to . We prove that, if the heat kernel on functions satisfies a Gaussian upper bound and if the negative part of the Ricci curvature is ε‐sub‐critical for some , then is bounded from to and is bounded from to for where depends on ε and on a constant appearing in the volume doubling property. A duality argument gives the boundedness of the Riesz transform from to for where Δ is the non‐negative Laplace–Beltrami operator. We also give a condition on to be ε‐sub‐critical under both analytic and geometric assumptions.  相似文献   

20.
《Mathematische Nachrichten》2018,291(5-6):908-927
Consider the Bessel operator with a potential on , namely We assume that and is a nonnegative function. By definition, a function belongs to the Hardy space if Under certain assumptions on V we characterize the space in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to for with no additional assumptions on the potential V.  相似文献   

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