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1.
In this paper for a positive real number α we consider two partial differential operators D and Dα on the half–plane
We define a generalized Fourier transform
associated with the operators D and Dα. We establish an analogue of Beurling–H?rmander’s Theorem for this transform
and we give some applications of this theorem. 相似文献
2.
It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class
() and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol
of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms
of pseudodifferential operators with -bounded symbols, yielding by an iteration argument the -boundedness of λ(A−λ)−1 in for some . To this end, elements of a symbolic and operator calculus of pseudodifferential operators with -bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential
operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on with operator valued coefficients. 相似文献
3.
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity 总被引:1,自引:0,他引:1
Andreas Fr?hlich 《Mathematische Annalen》2007,339(2):287-316
In this paper we establish a general weighted L
q
-theory of the Stokes operator in the whole space, the half space and a bounded domain for general Muckenhoupt weights . We show weighted L
q
-estimates for the Stokes resolvent system in bounded domains for general Muckenhoupt weights. These weighted resolvent estimates
imply not only that the Stokes operator generates a bounded analytic semigroup but even yield the maximal L
p
-regularity of in the respective weighted L
q
-spaces for arbitrary Muckenhoupt weights . This conclusion is archived by combining a recent characterisation of maximal L
p
-regularity by -bounded families due to Weis [Operator-valued Fourier multiplier theorems and maximal L
p
-regularity. Preprint (1999)] with the fact that for L
q
-spaces -boundedness is implied by weighted estimates. 相似文献
4.
Peer Christian Kunstmann 《Archiv der Mathematik》2008,91(2):178-186
We consider the Stokes operator A on unbounded domains of uniform C
1,1-type. Recently, it has been shown by Farwig, Kozono and Sohr that – A generates an analytic semigroup in the spaces , 1 < q < ∞, where for q ≥ 2 and for q ∈ (1, 2). Moreover, it was shown that A has maximal L
p
-regularity in these spaces for p ∈ (1,∞). In this paper we show that ɛ + A has a bounded H
∞-calculus in for all q ∈ (1, ∞) and ɛ > 0. This allows to identify domains of fractional powers of the Stokes operator.
Received: 12 October 2007 相似文献
5.
We study cyclicity of operators on a separable Banach space which admit a bicyclic vector such that the norms of its images
under the iterates of the operator satisfy certain growth conditions. A simple consequence of our main result is that a bicyclic
unitary operator on a Banach space with separable dual is cyclic. Our results also imply that if is the shift operator acting on the weighted space of sequences , if the weight ω satisfies some regularity conditions and ω(n) = 1 for nonnegative n, then S is cyclic if . On the other hand one can see that S is not cyclic if the series diverges. We show that the question of Herrero whether either S or S* is cyclic on admits a positive answer when the series is convergent. We also prove completeness results for translates in certain Banach spaces of functions on . 相似文献
6.
In this paper we prove the O’Neil inequality for the k-linear convolution f ⊗ g. By using the O’Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the k-linear convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness
of the k-sublinear fractional maximal operator M
Ω, α and k-linear fractional integral operator I
Ω, α with rough kernels from the spaces
V.S. Guliyev partially supported by the grant of INTAS (project 05-1000008-8157). 相似文献
7.
Veronica Felli Emmanuel Hebey Frédéric Robert 《NoDEA : Nonlinear Differential Equations and Applications》2005,12(2):171-213
Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we consider equations like
where
is a Paneitz-Branson type operator with constant coefficients α and aα, u is required to be positive, and
is critical from the Sobolev viewpoint. We define the energy function Em as the infimum of
over the u’s which are solutions of the above equation. We prove that Em (α ) →+∞ as α →+∞ . In particular, for any Λ > 0, there exists α0 > 0 such that for α ≥ α0, the above equation does not have a solution of energy less than or equal to Λ. 相似文献
8.
Multipliers and Cyclic Vectors in Bloch Type Spaces 总被引:6,自引:0,他引:6
In this paper we study the coefficient multipliers, pointwise multipliers and cyclic vectors in the Bloch type spaces B
α
and little Bloch type spaces
for 0 < α < ∞. We give several full characterizations of the coefficient multipliers (B
α
,B
β
) and
for 0 < α, β < ∞ and pointwise multipliers M(B
α
,B
β
) and
for 1 ≠ α, β ∈ (0,∞). We also obtain some properties of cyclic vectors for Bloch type spaces.
Dedicated to Professor Yu Zan HE on the occasion of his 65th birthday 相似文献
9.
Jun Zhang 《Annals of the Institute of Statistical Mathematics》2007,59(1):161-170
The family of α-connections ∇(α) on a statistical manifold equipped with a pair of conjugate connections and is given as . Here, we develop an expression of curvature R
(α) for ∇(α) in relation to those for . Immediately evident from it is that ∇(α) is equiaffine for any when are dually flat, as previously observed in Takeuchi and Amari (IEEE Transactions on Information Theory 51:1011–1023, 2005). Other related formulae are also developed.
The work was conducted when the author was on sabbatical leave as a visiting research scientist at the Mathematical Neuroscience
Unit, RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan. 相似文献
10.
Singular Integrals and Commutators in Generalized Morrey Spaces 总被引:1,自引:0,他引:1
Lubomiea Softova 《数学学报(英文版)》2006,22(3):757-766
11.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
12.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
13.
Let b be a BMO function, and the commutator of order k for the Weyl fractional integral. In this paper we prove weighted strong type (p, p) inequalities (p > 1) and weighted endpoint estimates (p = 1) for the operator and for the pairs of weights of the type (w, ), where w is any weight and is a suitable one-sided maximal operator. We also prove that, for weights, the operator is controlled in the L
p
(w) norm by a composition of the one-sided fractional maximal operator and the one-sided Hardy-Littlewood maximal operator iterated
k times. These results improve those obtained by an immediate application of the corresponding two-sided results and provide
a different way to obtain known results about the operators . The same results can be obtained for the commutator of order k for the Riemann-Liouville fractional integral
This research has been partially supported by Spanish goverment Grant MTM2005-8350-C03-02. The first author was also supported
by CONICET, ANPCyT and CAI+D-UNL. The second author was also supported by Junta de Andalucía Grant FQM 354. 相似文献
14.
Chong LI Genaro LOPEZ 《数学学报(英文版)》2006,22(3):741-750
Let B (resp. K, BC,KC) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem (F, G) is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC / G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B /B° (resp. K / B°, BC /B°, KC / B°) is a-porous in B (resp. K,BC, KC). Moreover, we prove that for most (in the sense of the Baire category) closed bounded subsets G of X, the set K / B° is dense and uncountable in K. 相似文献
15.
It has been known for a long time that the Deligne–Lusztig curves associated to the algebraic groups of type and defined over the finite field all have the maximum number of -rational points allowed by the Weil “explicit formulas”, and that these curves are -maximal curves over infinitely many algebraic extensions of . Serre showed that an -rational curve which is -covered by an -maximal curve is also -maximal. This has posed the problem of the existence of -maximal curves other than the Deligne–Lusztig curves and their -subcovers, see for instance Garcia (On curves with many rational points over finite fields. In: Finite Fields with Applications
to Coding Theory, Cryptography and Related Areas, pp. 152–163. Springer, Berlin, 2002) and Garcia and Stichtenoth (A maximal
curve which is not a Galois subcover of the Hermitan curve. Bull. Braz. Math. Soc. (N.S.) 37, 139–152, 2006). In this paper, a positive answer to this problem is obtained. For every q = n
3 with n = p
r
> 2, p ≥ 2 prime, we give a simple, explicit construction of an -maximal curve that is not -covered by any -maximal Deligne–Lusztig curve. Furthermore, the -automorphism group Aut has size n
3(n
3 + 1)(n
2 − 1)(n
2 − n + 1). Interestingly, has a very large -automorphism group with respect to its genus .
Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni, PRIN 2006–2007. 相似文献
16.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
17.
Min-Lin Lo 《Integral Equations and Operator Theory》2007,57(3):397-412
We consider the relationship between Gabor-Daubechies windowed Fourier localization operators
and Berezin-Toeplitz operators T
φ, using the Bargmann isometry β. For “window” w a finite linear combination of Hermite functions, and a very general class of functions φ, we prove an equivalence of the
form
by obtaining the exact formulas for the operator C and the linear differential operator D. 相似文献
18.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
19.
Gaspar Mora 《Mediterranean Journal of Mathematics》2005,2(3):315-325
Given a real function f of class
defined on the unit cube In=[0,1]n , n ≥ 2, our purpose consists in finding an algorithm to approximate to
by a dimensional reduction. The method deals with α-dense curves γα in the domain In with arbitrary small density α and a minimization-preserving operator T (briefly M.P.O.) applied to the univariable function
By reiterating the action of this M.P.O. we obtain an algorithm to determine a global minimizer t0* of fα. The value fα(t0*), taken as an approximation to f*, only depends on the density α of the curve chosen to densify the domain of the objective function. 相似文献
20.
Robert J. Taggart 《Mathematische Zeitschrift》2009,261(4):933-949
Suppose that {T
t
: t ≥ 0} is a symmetric diffusion semigroup on L
2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem
and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence. 相似文献