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1.
Various characterizations are given of the exponential Orlicz space L and the Orlicz‐Lorentz space L. By way of application we give a simple proof of the celebrated theorem of Brézis and Wainger concerning a limiting case of a Sobolev imbedding theorem.  相似文献   

2.
This paper is a continuation of [8]. We study weighted function spaces of type B and F on the Euclidean space Rn, where u is a weight function of at most exponential growth. In particular, u(χ (±|χ|) is an admissible weight. We deal with atomic decompositions of these spaces. Furthermore, we prove that the spaces B and F are isomorphic to the corresponding unweighted spaces B and F.  相似文献   

3.
This article deals with the LORENTZ-MARCINKIEWICZ operator ideal ?? generated by an additive s-function and the LORENTZ-MARCINKIEWICZ sequence space λq(φ). We give eigenvalue distributions for operators belonging to ?? (E, E) and we show the interpolation properties of ??-ideals. Furthermore, we study certain SCHAUDER bases in ?? (H, K), H and K Hilbert spaces.  相似文献   

4.
By using the LITTLEWOOD matrices A2n we generalize CLARKSON' S inequalities, or equivalently, we determine the norms ‖A2n: l(LP) → l(LP)‖ completely. The result is compared with the norms ‖A2n: ll‖, which are calculated implicitly in PIETSCH [6].  相似文献   

5.
The d-dimensional Hardy spaces Hp ( T × … × T ) (d = d1 + … + dkand a general summability method of Fourier series and Fourier transforms are introduced with the help of integrable functions θj having integrable Fourier transforms. Under some conditions on θj we show that the maximal operator of the θ-means of a distribution is bounded from Hp ( T × … × T ) to Lp ( T d) where p0 < p < ∞ and p0 < 1 is depending only on the functions θj. By an interpolation theorem we get that the maximal operator is also of weak type ( L1) (i = 1, …, k) where the Hardy space is defined by a hybrid maximal function and if k = 1. As a consequence we obtain that the θ-means of a function (log L)k–1 converge a.e. to the function in question. If k = 1 then we get this convergence result for all fL1. Moreover, we prove that the θ-means are uniformly bounded on the spaces Hp ( T × … × T ) whenever p0 <p < ∞, thus the θ-means converge to f in ( T × … × T ) norm. The same results are proved for the conjugate θ-means and for d-dimensional Fourier transforms, too. Some special cases of the θ-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, Riemann, de La Vallée-Poussin, Rogosinski and Riesz summations.  相似文献   

6.
This paper is the continuation of [17]. We investigate mapping and spectral properties of pseudodifferential operators of type Ψ with χ χ ? ? and 0 ≤ γ ≤ 1 in the weighted function spaces B (?n, w(x)) and F (?n, w(x)) treated in [17]. Furthermore, we study the distribution of eigenvalues and the behaviour of corresponding root spaces for degenerate pseudodifferential operators preferably of type b2(x) b(x, D) b1(x), where b1(x) and b2(x) are appropriate functions and b(x, D) ? Ψ. Finally, on the basis of the Birman-Schwinger principle, we deal with the “negative spectrum” (bound states) of related symmetric operators in L2.  相似文献   

7.
We consider a boundary problem for an elliptic system in a bounded region Ω ? ?n and where the spectral parameter is multiplied by a discontinuous weight function ω (x) = diag(ω1(x), …, ωN (x)). The problem is considered under limited smoothness assumptions and under an ellipticity with parameter condition. Recently, this problem was studied under the assumption that the ωj (x)–1 are essentially bounded in Ω. In this paper we suppose that ω (x) vanishes identically in a proper subregion Ω of Ω and that the ωj (x)–1 are essentially bounded in . Then by using methods which are a variant of those used in constructing the Calderón projectors for the boundary Γ of Ω, we shall derive results here which will enable us in a subsequent work to apply the ideas of Calderón to develop the spectral theory associated with the problem under consideration here (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

8.
The paper deals with sharp embeddings of the spaces B and F into rearrangement-variant spaces and related Hardy inequalities. Here (1/p, s) belongs to the interior of the shaded invariant spaces region in the Figure  相似文献   

9.
In this paper we prove subelliptic estimates for operators of the form Δx + λ2 (x)S in ?N = ? × ?, where the operator S is an elliptic integro - differential operator in ?N and λ is a nonnegative Lipschitz continuous function.  相似文献   

10.
We study weakly ramified extensions of ℚ with Galois group CCp, where p is an odd prime. In particular, we describe an infinite family of such extensions when p = 3.  相似文献   

11.
For a quartic double solid we study the parameter space of conics (i.e. of smooth rational curves CZ such that C · φ*O(1) = 2). This parameter space is naturally fibred (with disconnected fibres) over Pˇ3. We study the monodromy of the fibres and determine this way the irreducible components of the parameter space.  相似文献   

12.
We compute the absolutely L – summing norms of the diagonal operators acting on lr (1 ≤ q, r < ∞) and determine the limit orders of the absolutely Lexp – summing operators.  相似文献   

13.
Symmetry- and selfadjointness-conditions are derived for ordinary differential-integral-interface operators under integral-interface conditions. Criteria for the existence of selfadjoint extensions in L×L are given. These extensions are characterized in a constructive way. The main tools are some extension-theorems for linear relations (subspaces), wich are developed in section 2.  相似文献   

14.
In this paper we study weighted function spaces of type B(?n, Q(x)) and F(?n, Q(x)), where Q(x) is a weight function of at most polynomial growth. Of special interest are the weight functions Q(x) = (1 + |x|2)α/2 with α ? ?. The main result deals with estimates for the entropy numbers of compact embeddings between spaces of this type.  相似文献   

15.
We study the maximal function Mf(x) = sup |f(x + y, t)| when Ω is a region in the (y,t) Ω upper half space R and f(x, t) is the harmonic extension to R+N+1 of a distribution in the Besov space Bαp,q(RN) or in the Triebel-Lizorkin space Fαp,q(RN). In particular, we prove that when Ω= {|y|N/ (N-αp) < t < 1} the operator M is bounded from F (RN) into Lp (RN). The admissible regions for the spaces B (RN) with p < q are more complicated.  相似文献   

16.
A k‐star is the graph K1,k. We prove a general theorem about k‐star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k‐star factorizations of any power (Kq)s of a complete graph with prime power order q, products C × C ×··· × C of k cycles of arbitrary lengths, and any power (Cr)s of a cycle of arbitrary length. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 59–66, 2001  相似文献   

17.
Let (Xn) be a sequence of infinite-dimensional BANACH spaces. We prove that has a non-locally complete quotient if X1 is not quasi-reflexive.  相似文献   

18.
It is shown that for 0<p ≥ 1, the trigonometric polynomials are dense in H, the space of B-valued harmonic functions with non-tangential maximal function in Lp, if and only if the Banach space B has the Radon-Nikodym property (R.N.P.). This extends known results for 1 <p < ∞. We also show that H coincides with the corresponding atomic space if and only if B has the R.N.P.  相似文献   

19.
Claudia M. Gariboldi  Domingo A. Tarzia 《PAMM》2007,7(1):1060403-1060404
We consider a steady-state heat conduction problem Pα withmixed boundary conditions for the Poisson equation in a bounded multidimensional domain Ω depending of a positive parameter α which represents the heat transfer coefficient on a portion Γ1 of the boundary of Ω. We consider, for each α > 0, a cost function Jα and we formulate boundary optimal control problems with restrictions over the heat flux q on a complementary portion Γ2 of the boundary of Ω. We obtain that the optimality conditions are given by a complementary free boundary problem in Γ2 in terms of the adjoint state. We prove that the optimal control q and its corresponding system state u and adjoint state p for each α are strongly convergent to qop, u and p in L22), H1(Ω), and H1(Ω) respectively when α → ∞. We also prove that these limit functions are respectively the optimal control, the system state and the adjoint state corresponding to another boundary optimal control problem with restrictions for the same Poisson equation with a different boundary condition on the portion Γ1. We use the elliptic variational inequality theory in order to prove all the strong convergences. In this paper, we generalize the convergence result obtained in Ben Belgacem-El Fekih-Metoui, ESAIM:M2AN, 37 (2003), 833-850 by considering boundary optimal control problems with restrictions on the heat flux q defined on Γ2 and the parameter α (which goes to infinity) is defined on Γ1. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

20.
Let X be a projective algebraic manifold of dimension n (over C), CH1(X) the Chow group of algebraic cycles of codimension l on X, modulo rational equivalence, and A1(X) ? CH1(X) the subgroup of cycles algebraically equivalent to zero. We say that A1(X) is finite dimensional if there exists a (possibly reducible) smooth curve T and a cycle z∈CH1(Γ × X) such that z*:A1(Γ)-A1(X) is surjective. There is the well known Abel-Jacobi map λ1:A1(X)-J(X), where J(X) is the lth Lieberman Jacobian. It is easy to show that A1(X)→J(X) A1(X) finite dimensional. Now set with corresponding map A*(X)→J(X). Also define Level . In a recent book by the author, there was stated the following conjecture: where it was also shown that (?) in (**) is a consequence of the General Hodge Conjecture (GHC). In this present paper, we prove A*(X) finite dimensional ?? Level (H*(X)) ≤ 1 for a special (albeit significant) class of smooth hypersurfaces. We make use of the family of k-planes on X, where ([…] = greatest integer function) and d = deg X; moreover the essential technical ingredients are the Lefschetz theorems for cohomology and an analogue for Chow groups of hypersurfaces. These ingredients in turn imply very special cases of the GHC for our choice of hypersurfaces X. Some applications to the Griffiths group, vanishing results, and (universal) algebraic representatives for certain Chow groups are given.  相似文献   

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