共查询到20条相似文献,搜索用时 578 毫秒
1.
V.B Headley 《Journal of Mathematical Analysis and Applications》1985,108(1):283-292
Let D(?) be the Doob's class containing all functions f(z) analytic in the unit disk Δ such that f(0) = 0 and lim on an arc A of ?Δ with length . It is first proved that if f?D(?) then the spherical norm ∥ f ∥ = supz?Δ, where C1 = limn→∞. Next, U represents the Seidel's class containing all non-constant functions f(z) bounded analytic in Δ such that almost everywhere. It is proved that inff?U∥f∥ = 0, and if f has either no singularities or only isolated singularities on ?Δ, then ∥f∥ ? C1. Finally, it is proved that if f is a function normal in Δ, namely, the norm ∥f∥< ∞, then we have the sharp estimate ∥fp∥ ? p∥f∥, for any positive integer p. 相似文献
2.
Steven Zelditch 《Journal of Functional Analysis》1983,50(1):67-80
We prove a Szegö-type theorem for some Schrödinger operators of the form with V smooth, positive and growing like . Namely, let πλ be the orthogonal projection of L2 onto the space of the eigenfunctions of H with eigenvalue ?λ; let A be a 0th order self-adjoint pseudo-differential operator relative to Beals-Fefferman weights and with total symbol a(x, ξ); and let f∈C(). Then (assuming one limit exists). 相似文献
3.
Robert S Strichartz 《Journal of Functional Analysis》1982,49(1):91-127
The composition of two Calderón-Zygmund singular integral operators is given explicitly in terms of the kernels of the operators. For φ?L1(Rn) and ε = 0 or 1 and ∝ φ = 0 if ε = 0, let Ker(φ) be the unique function on Rn + 1 homogeneous of degree ?n ? 1 of parity ε that equals φ on the hypersurface x0 = 1. Let Sing(φ, ε) denote the singular integral operator , which exists under suitable growth conditions on ? and φ. Then Sing(φ, ε1) Sing(ψ, ε2)f = ?2π2(∝ φ)(∝ ψ)f + Sing(A, ε1, + ε2)f, where (with notation ). This result is used to show that the mapping ψ → A is a classical pseudo-differential operator of order zero if φ is smooth, with top-order symbol , where θ(ξ) is a cut-off function. These results are generalized to singular integrals with mixed homogeneity. 相似文献
4.
Sanford S Miller Petru T Mocanu Maxwell O Reade 《Journal of Mathematical Analysis and Applications》1975,51(1):33-42
Suppose that f(z) = z + a2z2 + ··· + anzn + ··· is regular in the unit disc , and further let α ? 0 and k ? 2. If , then f(z) is said to belong to the class MV[α, k]. This class contains many of the special classes of regular and univalent functions. The authors determine the Hardy classes of which f(z), f′(z) and f″(z) belong and obtain growth estimates of an. 相似文献
5.
Raymond C Roan 《Journal of Functional Analysis》1980,39(1):67-74
Let α ? 0 and let . Then D(α) is a subalgebra of l1. We discuss the weak-1 generators of D(α). We use some of our techniques to prove that if ? is a weak-1 generator of H∞ and ∥ ? ∥∞ ? 1, then the composition operator C? on the Dirichlet space has dense range. 相似文献
6.
S.K. Bajpai Joseph Tanne Donald Whittier 《Journal of Mathematical Analysis and Applications》1974,48(3):736-742
Let f(z), an analytic function with radius of convergence R (0 < R < ∞) be represented by the gap series ∑k = 0∞ckzλk. Set and define the growth constants ?, λ, T, t by , and if 0 < ? < ∞, . Then, assuming 0 < t < T < ∞, we obtain a decomposition theorem for f(z). 相似文献
7.
Tibor Krisztin 《Journal of Mathematical Analysis and Applications》1985,109(2):509-521
Let be the classes of univalent functions defined in , which are convex of order β, starlike of order β and close-to-convex of order β type λ. Let . We discuss the properties of the function f when this function F belongs to the class K(β, λ) and its various subclasses. 相似文献
8.
9.
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
10.
Pascal Cherrier 《Journal of Functional Analysis》1983,53(3):231-245
On a compact Kähler manifold of complex dimension m ? 2, let us consider the change of Kähler metric . Let F?C∞(V × R) be a function everywhere > 0 and v a real number ≠ 0. When for all (x, t) ?V × ] ?∞, t0], where C and t0 are constants and , one exhibits a function φ?C∞ (V) such that the determinants of the metrics g and . 相似文献
11.
Arthur Lubin 《Journal of Functional Analysis》1974,17(4):388-394
Let m and vt, 0 ? t ? 2π be measures on T = [0, 2π] with m smooth. Consider the direct integral = ⊕L2(vt) dm(t) and the operator on , where e(s, t) = exp ∫st ∫Tdvλ(θ) dm(λ). Let μt be the measure defined by for all continuous ?, and let ?t(z) = exp[?∫ (eiθ + z)(eiθ ? z)?1dμt(gq)]. Call {vt} regular iff for all for 1 a.e. 相似文献
12.
Curtis Greene 《Journal of Combinatorial Theory, Series A》1976,20(1):69-79
For any partially ordered set P, let denote the cardinality of the largest subset of P obtained by taking the union of k antichains (chains). Then there exists a partition Δ = {Δl ? Δ2 > … ? Δl} of | P | such that dk(P) = Δ1 + Δ2 + … + Δk and for each k, where denotes the partition conjugate to Δ. This result can be used to prove a general class of “Dilworth-type” theorems for subfamilies of P. 相似文献
13.
Zeev Schuss 《Journal of Mathematical Analysis and Applications》1977,59(2):227-241
Let A and B be uniformly elliptic operators of orders 2m and 2n, respectively, m > n. We consider the Dirichlet problems for the equations (?2(m ? n)A + B + λ2nI)u? = f and (B + λ2nI)u = f in a bounded domain Ω in Rk with a smooth boundary ?Ω. The estimate is derived. This result extends the results of [7, 9, 10, 12, 14, 15, 18]by giving estimates up to the boundary, improving the rate of convergence in ?, using lower norms, and considering operators of higher order with variable coefficients. An application to a parabolic boundary value problem is given. 相似文献
14.
For parabolic initial boundary value problems various results such as , where u satisfies , are demonstrated via the maximum principle and potential theoretic estimates. 相似文献
15.
Christer Borell 《Journal of Mathematical Analysis and Applications》1973,43(2):419-440
Let ψ be convex with respect to ?, B a convex body in Rn and f a positive concave function on B. A well-known result by Berwald states that (1) if ξ is chosen such that .The main purpose in this paper is to characterize those functions f : B → R+ such that (1) holds. 相似文献
16.
17.
Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
18.
Using results from the theory of B-splines, various inequalities involving the nth order divided differences of a function f with convex nth derivative are proved; notably, , where z is the center of mass . 相似文献
19.
Juan C. Peral 《Journal of Functional Analysis》1980,36(1):114-145
Let u(x, t) be the solution of utt ? Δxu = 0 with initial conditions . Consider the linear operator . (Here g = 0.) We prove for t fixed the following result. Theorem 1: T is bounded in Lp if and only if . Theorem 2: If the coefficients are variables in C and constant outside of some compact set we get: (a) If n = 2k the result holds for . (b) If n = 2k ? 1, the result is valid for . This result are sharp in the sense that for p such that we prove the existence of in such a way that . Several applications are given, one of them is to the study of the Klein-Gordon equation, the other to the completion of the study of the family of multipliers and finally we get that the convolution against the kernel is bounded in H1. 相似文献
20.
Richard Lavine 《Journal of Functional Analysis》1973,12(1):30-54
Absolute continuity in (0, ∞) for Schrödinger operators ? Δ + V(x), with long range potential V = V1 + V2 such that , ? > 0, as , is shown by proving estimates on resolvents near the real axis. Completeness of the modified wave operators for a superposition of Coulomb potentials also follows. Singular local behavior of V is allowed. 相似文献