共查询到20条相似文献,搜索用时 203 毫秒
1.
Bao Qin Li 《Mathematische Zeitschrift》2008,258(4):763-771
We show that meromorphic solutions f, g of f
2 + g
2 = 1 in C2 must be constant, if f
z2 and g
z1 have the same zeros (counting multiplicities). We also apply the result to characterize meromorphic solutions of certain
nonlinear partial differential equations. 相似文献
2.
G. P. Crespi I. Ginchev M. Rocca 《Journal of Optimization Theory and Applications》2004,123(3):479-496
Let E be a linear space, let K
E and f:K . We formulate in terms of the lower Dini directional derivative problem GMVI (f
,K
), which can be considered as a generalization of MVI (f
,K
), the Minty variational inequality of differential type. We investigate, in the case of K star-shaped (SS), the existence of a solution x
* of GMVI (f
K
) and the property of f to increase-along-rays starting at x
*, fIAR (K,x
*). We prove that the GMVI (f
,K
) with radially l.s.c. function f has a solution x
* ker K if and only if fIAR (K,x
*). Further, we prove that the solution set of the GMVI (f
,K
) is a convex and radially closed subset of ker K. We show also that, if the GMVI (f
,K
) has a solution x
*K, then x
* is a global minimizer of the problem min f(x), xK. Moreover, we observe that the set of the global minimizers of the related optimization problem, its kernel, and the solution set of the variational inequality can be different. Finally, we prove that, in the case of a quasiconvex function f, these sets coincide. 相似文献
3.
N. Fusco G. Moscariello C. Sbordone 《Calculus of Variations and Partial Differential Equations》2008,33(3):377-390
We show that the limit f of a weakly convergent sequence of W
1,1 homeomorphisms f
j
with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity
of the distortions is deduced both in case of outer and inner distortion. 相似文献
4.
Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ. 相似文献
5.
For a PL homeomorphism f with irrational rotation number , the following properties are equivalent(i) f is conjugate to the rotation by through a piecewise C
1 homeomorphism,(ii) the number of break points of f
n
is bounded by some constant that doesnt depend on n,(iii) f is conjugate to an affine 2-intervals exchange transformation (with rotation number ) through a PL homeomorphism,(iv) f is conjugate to the rotation by through a piecewise analytic homeomorphism. 相似文献
6.
Małgorzata Stawiska 《Central European Journal of Mathematics》2005,3(3):398-403
We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints. 相似文献
7.
Jesse Peterson 《Inventiones Mathematicae》2009,175(2):417-433
We introduce the notion of L
2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing
of 1-cohomology into the left regular representation of a group. We show that L
2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that if M is a free product
of diffuse von Neumann algebras, or if M=LΓ where Γ is a finitely generated group with β1
(2)(Γ)>0, then any nonamenable regular subfactor of M is prime and does not have properties Γ or (T). In particular this gives a new approach for showing solidity for a free group
factor thus recovering a well known recent result of N. Ozawa. 相似文献
8.
We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献
9.
Let G be a locally compact group. For 1 < p < ∞, it is well-known that f * g exists and belongs to Lp(G) for all f, g
Lp
(G) if and only if G is compact. Here, for 2 < p < ∞, we show that f * g exists for all f, g
Lp(G) if and only if G is compact. We also show that this result does not remain true for 1 < p ≤ 2.
Received: 23 April 2006 相似文献
10.
Bao Qin Li 《Israel Journal of Mathematics》2004,143(1):131-140
We describe entire solutions inC
n
of non-linear partial differential equations of the form (∂w/∂z
j
)
k
=f(w), wheref is a meromorphic function in the complex plane andk is a positive integer.
Supported in part by the National Science Foundation (USA) Grant DMS-0100486. 相似文献
11.
For a fixed prime p, let C
p
denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f
2 (x) + B (x) g
2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method. 相似文献
12.
The purpose of this paper is to study the L
2 boundedness of operators of the form f ↦ ψ(x) ∫ f (γ
t
(x))K(t)dt, where γ
t
(x) is a C
∞ function defined on a neighborhood of the origin in (t, x) ∈ ℝ
N
× ℝ
n
, satisfying γ
0(x) ≡ x, ψ is a C
∞ cut-off function supported on a small neighborhood of 0 ∈ ℝ
n
, and K is a “multi-parameter singular kernel” supported on a small neighborhood of 0 ∈ ℝ
N
. The goal is, given an appropriate class of kernels K, to give conditions on γ such that every operator of the above form is bounded on L
2. The case when K is a Calderón-Zygmund kernel was studied by Christ, Nagel, Stein, and Wainger; we generalize their conditions to the case
when K has a “multi-parameter” structure. For example, when K is given by a “product kernel.” Even when K is a Calderón- Zygmund kernel, our methods yield some new results. This is the first paper in a three part series, the later
two of which are joint with E. M. Stein. The second paper deals with the related question of L
p
boundedness, while the third paper deals with the special case when γ is real analytic. 相似文献
13.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
14.
Natalio H. Guersenzvaig 《Israel Journal of Mathematics》2009,169(1):109-123
In this paper, very simple sufficient conditions for the irreducibility of f(X
r
) over an arbitrary unique factorization domain Z are established. 相似文献
15.
It is proved that the complex double Fourier series of an integrable functionf(x, y) with coefficients cjk satisfying certain conditions, will converge in L1-norm. The conditions used here are the combinations of Tauberian condition of Hardy-Karamata kind and its limiting case.
This paper extends the result of Bray [1] to complex double Fourier series.
An erratum to this article is available at . 相似文献
16.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data,
f
D
, has one derivative in L
p
(D) of the boundary and the Neumann data, f
N
, is in L
p
(N). We find a p
0 > 1 so that for p in an interval (1, p
0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L
p
.
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation. 相似文献
17.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
18.
Yun Qing Xu 《数学学报(英文版)》2009,25(8):1325-1336
A Latin squares of order v with ni missing sub-Latin squares (holes) of order hi (1 〈= i 〈 k), which are disjoint and spanning (i.e. ∑k i=l1 nihi = v), is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by (h1n1 h2n2…hknk ). If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS(T). It has been proved that 3-HMOLS(2n31) exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS(2nu1) with u ≥ 4, and prove that 3-HMOLS(2~u1) exist if n ≥ 54 and n ≥7/4u + 7. 相似文献
19.
Oscar Mario Perdomo 《Geometriae Dedicata》2007,129(1):23-34
In this paper we prove that if is a minimal immersion of a compact surface and , for some homogeneous polynomial f of degree 3 on R
4, then, M is a torus and is one of the examples given by Lawson (1970, Complete minimal surfaces in S
3. Ann. Math. 92(2), 335–374).
相似文献
20.
We study the L
1
-lower semicontinuity in BV of an integral functional of the type
. Our assumptions on f extend previous results recently obtained by Gori, Maggi and Marcellini in the case where the above functional is restricted to W
1,1
. 相似文献