实单位球上关于Green函数的M(o)bius不变空间Qp,o

讨论了实单位球上的M调和函数.利用Green函数定义了函数空间Qp,o.通过对p变化时Qp,o的演化的讨论,得到函数空间VMOh及β0的一种统一的刻划.     

Rearrangement invariant subspaces of Lorentz function spaces

The main result is that for 2≦q≦p<∞ the only subspaces of the Lorentz function spaceL _pq [0, 1] which are isomorphic to r.i. function spaces on [0, 1] are, up to equivalent renormings,L _pq [0, 1] andL ₂[0, 1].     

Wavelet bases in rearrangement invariant function spaces

We point out that the well known characterization of spaces () in terms of orthogonal wavelet bases extends to any separable rearrangement invariant Banach function space on (equipped with Lebesgue measure) with nontrivial Boyd's indices. Moreover we show that such bases are unconditional bases of .

     

Nikolskii-type inequalities for shift invariant function spaces

Let be a vectorspace of complex-valued functions defined on of dimension over . We say that is shift invariant (on ) if implies that for every , where on . In this note we prove the following.

Theorem. Let be a shift invariant vectorspace of complex-valued functions defined on of dimension over . Let . Then

for every and

     

Martingale inequalities in rearrangement invariant function spaces

The Burkholder-Davis-Gundy equivalence of the square function and maximal function of a martingale is extended to the setting of rearrangement invariant function spaces. Supported in part by NSF DMS-8703815 and U.S.-Isreal Binational Science Foundation. Supported in part by U.S.-Israel Binational Science Foundation.     

On Rosenthal's inequality and rearrangement invariant spaces

Khabarovsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 1, pp. 32–37, January–February, 1993.     

On the Fourier transformation on spaces of (p,q)-multipliers

LetG denote a locally compact abelian topological group. The aim of the present paper is to prove an “intermediate” result between two well-known results ofL. Hörmander andG. I. Gaudry concerning the structure of the spaces ?_G?μ?t ^p,q (G).     

On projective spaces PG(r, q) with r ≥ 4

In this paper a characterization of PG(r, q), r ≥ 4, in terms of planar spaces is given. Domenico Olanda: This research was carried out within the activity of INdAM-GNSAGA and supported by the Italian Ministry M.I.U.R.     

The majorization function and the index of invariant sub spaces in the Bergman spaces

The index of an invariant subspace ℳ of a Banach space of analytic functions in the open unit disc is defined by indℳ = dimℳ/zℳ. In this paper, we provide a strong link between high index and nontangential boundary behaviour of the functions in an invariant subspace. Work of the first author was partially supported by the Royal Swedish Academy of Sciences; work of the second and third authors was supported by the National Science Foundation.     

On sizes of complete caps in projective spaces PG(n, q) and arcs in planes PG(2, q)

More than thirty new upper bounds on the smallest size t ₂(2, q) of a complete arc in the plane PG(2, q) are obtained for (169 ≤ q ≤ 839. New upper bounds on the smallest size t ₂(n, q) of the complete cap in the space PG(n, q) are given for n = 3 and 25 ≤ q ≤ 97, q odd; n = 4 and q = 7, 8, 11, 13, 17; n = 5 and q = 5, 7, 8, 9; n = 6 and q = 4, 8. The bounds are obtained by computer search for new small complete arcs and caps. New upper bounds on the largest size m ₂(n, q) of a complete cap in PG(n, q) are given for q = 4, n = 5, 6, and q = 3, n = 7, 8, 9. The new lower bound 534 ≤ m ₂(8, 3) is obtained by finding a complete 534-cap in PG(8, 3). Many new sizes of complete arcs and caps are obtained. The updated tables of upper bounds for t ₂(n, q), n ≥ 2, and of the spectrum of known sizes for complete caps are given. Interesting complete caps in PG(3, q) of large size are described. A proof of the construction of complete caps in PG(3, 2 ^h ) announced in previous papers is given; this is modified from a construction of Segre. In PG(2, q), for q = 17, δ = 4, and q = 19, 27, δ = 3, we give complete ${(\frac{1}{2}(q + 3) + \delta)}$ -arcs other than conics that share ${\frac{1}{2}(q + 3)}$ points with an irreducible conic. It is shown that they are unique up to collineation. In PG(2, q), ${{q \equiv 2}}$ (mod 3) odd, we propose new constructions of ${\frac{1}{2} (q + 7)}$ -arcs and show that they are complete for q ≤ 3701.     

(H,R)-Lie coalgebras and (H,R)-Lie bialgebras

Given an (H,R)-Lie coalgebra Γ, we construct (H,R _T )-Lie coalgebra Γ^T through a right cocycle T, where (H,R) is a triangular Hopf algebra, and prove that there exists a bijection between the set of (H,R)-Lie coalgebras and the set of ordinary Lie coalgebras. We also show that if (L, [, ], Δ, R) is an (H,R)-Lie bialgebra of an ordinary Lie algebra then (L ^T , [, ], Δ_T, R _T ) is an (H,R _T )-Lie bialgebra of an ordinary Lie algebra.     

On convolution operators leavingL p,λ spaces invariant

Summary It is shown that certain convolution operators, including the Hilbert transform in the one dimensional case, leave invariant the L^p,λ spaces studied by Campanato, Stampacchia and others.     

On the smallest non-trivial tight sets in Hermitian polar spaces H(d,q2), d even

We show that every $x$-tight set of a Hermitian polar spaces $\mathrm{H}(2n,q^2)$, $n\ge 2$, is the union of $x$ disjoint generators of the polar space provided that $x\le \frac{1}{2}(q+1)$. This was known before only when $n\in \{2,3\}$. This result is a contribution to the conjecture that the smallest $x$-tight set of $H(2n,q^2)$ that is not a union of disjoint generators occurs for $x=q+1$ and is for sufficiently large $q$ an embedded subgeometry.     

Elementary aspects ofB p,q s (Kn) andF p,q s (Kn) spaces

In the first part of this paper, we discuss some properties of S^Ω(K_n), L _P ^Ω (K_n) and L _P ^Ω (K_n;l_q) spaces, give the Plancherel-Polya-Nikol’skij type inequalities and some multiplier theorems. In the second part of this paper, using the results of Part I we prove some preliminary results for the spaces B _p,q ^s (K_n) and F _p,q ^s (K_n).