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1.
Cesare Parenti 《Annali di Matematica Pura ed Applicata》1972,93(1):391-406
Summary For a class of operators described in § 2 we study an elliptic boundary value problem in an unbounded domain ofR
n (half space). The main result is established using pseudo-differential techniques.
Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.
Entrata in Redazione il 4 maggio 1972. 相似文献
2.
By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established. 相似文献
3.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
4.
G. J. Rieger 《Mathematische Nachrichten》1997,186(1):225-242
In §1 we study Figure 1 for variable h. In §2 and §3 this is combined with Ford-circles (Figure 2) and the choice h = 0 (Figure 3). In §4 a limit is evaluated. In §5 we treat Figure 5 (“Ford-circles inside the unit-circle”) and a technical application. In §6 contains various modular figures (Figures 7, 8, 9). §7 treats synchronous rotation of Figure 1 and Eoing from R2 to R3; the rotating upper half-plane of C corresponds then to the unit-sphere. In §8 a sphere-packing on C is introduced. Finally in §9 a sphere-packing inside the unit-sphere arises. 相似文献
5.
For 0<p<∞, let Hp(R
n) denote the Lebesgue space for p>1 and the Hardy space for p ≤1. In this paper, the authors study Hp(R
n)×Hq(R
n)→Hr(R
n) mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the
standard fractional integral with the Calderón-Zygmund operator. The authors prove that such mapping properties hold if and
only if these operators satisfy certain cancellation conditions.
Supported by the NNSF and the National Education Comittee of China. 相似文献
6.
Jia-cheng Lan 《应用数学学报(英文版)》2005,21(4):615-622
In this paper, the author discusses the multilinear singular integrals with certain θ-type Calderdn- Zygmund operators and obtain the boundedness from weak H^1 (R^n) to weak L^1 (R^n). 相似文献
7.
§ 1 Introduction and main resultsLet Sn- 1 be the unitsphere in Rn(n≥ 2 ) equipped with normalized Lebesgue measure dσ= dσ(z′) .We say that a functionΩ(x,z) defined on Rn× Rnbelongs to L∞ (Rn)× Lr(Sn- 1 )(r≥ 1 ) ,ifΩ(x,z) satisfies the following two conditions,(i) for any x,z∈Rnandλ>0 ,there hasΩ(x,λz) =Ω(x,z) ;(ii)‖Ω‖L∞(Rn)× Lr(Sn- 1) :=supx∈ Rn∫Sn- 1|Ω(x,z′) | rdσ(z′) 1 / r<∞ .For 0 <α相似文献
8.
《Quaestiones Mathematicae》2013,36(1-2):237-257
Abstract N. Dunford and J.T. Schwartz gave a complete characterization of those matrices of (bounded) Fourier multiplier operators acting in L 2(RN) n which are spectral operators, [4; ch. XV]. In the present note this characterization is extended to the setting of LP(G)n , where G is a locally compact abelian group and 1 < p < ∞; see Theorem 2. 相似文献
9.
Yulan Jiao 《分析论及其应用》2010,26(3):261-277
In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the Lp(Rn) (1 < p < ∞) boundedness and a weak type L log L estimate for the corresponding maximal operator. 相似文献
10.
Jean -Bertrand Kammerer 《Annali di Matematica Pura ed Applicata》1985,142(1):215-261
Summary
The purpose of this paper is to study, in intrinsic way, the Moyal's product, defined in the flat space
R
2n. This product is defined here with the twisted convolution and the Fourier transform. The S(R
2n) and L2(R
2n) spaces are*5-algebras. Because of this definition, the*V-product of some tempered distributions is defined. Let O
M
v
be the set of multiplication operators in S(R
2n). By transposition, the S(R
2n) space is a right-module on O
M
v
. The support of f*v g is different from the support of f·g; under large enough hypotheses, there is a Taylor's formula for the star-product function of the v variable. The v space of the multiplication operators in L2(R
2n) is defined here as the space of tempered distributions, the image of which is the set of bounded operators in L2(R
2n) by the Weyl map. After the study of v space, it is possible to show the spectral resolution of the real elements of v or of O
M
v
, which satisfies a, probably superfluous, hypothesis. 相似文献
11.
《代数通讯》2013,41(5):2381-2401
Abstract Let 𝒪 be a discrete valuation ring whose residue field 𝒪/𝔭 is finite and has odd characteristic. Let l be a positive integer. Set R = 𝒪/𝔭 l and let R = R[θ] be the ring obtained by adjoining to R a square root of a non-square unit. Consider the involution σ of R that fixes R elementwise and sends θ to ? θ. Let V be a free R-module of rank n > 0 endowed with a non-degenerate hermitian form ( , ) relative to σ. Let U n (R) be the subgroup of GL(V) that preserves ( , ). Let SU n (R) be the subgroup of all g ∈ U n (R) whose determinant is equal to one. Let Ψ be the Weil character of U n (R). All irreducible constituents of Ψ are determined. An explicit character formula is given for each of them. In particular, all character degrees are computed. For n > 2 the corresponding results are also obtained for the restriction of Ψ to SU n (R). 相似文献
12.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
13.
Lucyna Szczepanik 《代数通讯》2013,41(9):3359-3367
ABSTRACT In this note it is proved that certain level sets of some real proper polynomial maps are nothing but spheres. As an application of this, we provide new proofs of Theorems 1.1, 1.2 and of the fundamental theorem of algebra. In addition, we show that every strictly convex (concave) polynomial map is proper. The latter implies that every real polynomial map g(x): R n → R n , whose Jacobian matrix is symmetric and has nonzero eigenvalues of the same sign, is a homeomorphism of R n onto R n . 相似文献
14.
In this paper we prove a well-posedness result for the Cauchy problem. We study a class of first order hyperbolic differential
[2] operators of rank zero on an involutive submanifold ofT
*
R
n+1-{0} and prove that under suitable assumptions on the symmetrizability of the lifting of the principal symbol to a natural
blow up of the “singular part” of the characteristic set, the operator is strongly hyperbolic. 相似文献
15.
Paolo Boggiatto 《Annali di Matematica Pura ed Applicata》1996,171(1):15-40
The theory of the Sobolev spacesH
m
p
(R
n
) (mR,p
polyhedron in
R
2n
)of [BG]is revisited here in the frame of new classes of pseudodifferential operators related to the same polyhedron
p.These operators generalize to corresponding classes of Fourier integral operators, for which we present the main lines of a symbolic calculus and results of continuity on the
H
m
p
(R
n
) spaces. 相似文献
16.
The Hilbert and Riesz transforms can be characterized up to scalar as the translation invariant operators that satisfy additionally
certain relative invariance of conformal transformation groups. In this article, we initiate a systematic study of translation
invariant operators from group theoretic viewpoints, and formalize a geometric condition that characterizes specific multiplier
operators uniquely up to scalar by means of relative invariance of affine subgroups. After providing some interesting examples
of multiplier operators having “large symmetry”, we classify which of these examples can be extended to continuous operators
on L
p
(R
n
) (1 < p < ∞).
T. Kobayashi was partially supported by Grant-in-Aid for Scientific Research 18340037, Japan Society for the Promotion of
Science. A. Nilsson was partially supported by Japan Society for the Promotion of Science. 相似文献
17.
18.
Frank Loose 《代数通讯》2013,41(7):2395-2416
Abstract A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a n ≠ 0 and a n R = r(l(a n )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 n (R) is left GP-injective. 相似文献
19.
Tsiu-Kwen Lee 《代数通讯》2013,41(2):661-669
ABSTRACT Let R be a prime algebra of characteristic not 2, and let δ be a q-skew σ-derivation of R. We show that if δ2n = 0 and q n ≠ ?1, then δ2n?1 = 0. 相似文献
20.
We consider quite general h-pseudodifferential operators on R
n
with small random perturbations and show that in the limit h → 0 the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The first author has previously
obtained a similar result in dimension 1. Our class of perturbations is different. 相似文献