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Summary Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f Lp, 1p2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to falmost everywhere for Re(z)>(l, p). The critical index (l, p) is the same as in the classical result of Stein in the Euclidean case.The first author was supported by funds of the Ministero della Pubblica Istruzione. The work was done while the second author was a member of the Mathematical Sciences Research Institute at Berkeley, with a fellowship from the Consiglio Nazionale delle Ricerehe. 相似文献
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Zhu Fuliu 《数学年刊B辑(英文版)》1998,19(1):21-34
OSCILLATINGMULTIPLIERSONNONCOMPACTRIEMANNIANSYMMETRICSPACESL(3,IH)/Sp(3)ZHUFULIUManuscriptreceivedJuly28,1995.RevisedApril... 相似文献
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Feng Dai 《Constructive Approximation》2005,22(3):417-436
Let $\sigma_k^\delta$ denote the Cesaro means of order $\delta > -1$ of the spherical harmonic expansions on the unit sphere $S^{d-1}$, and let $E_j(f, H^1)$ denote the best approximation of $f$ in the Hardy space $H^1(S^{d-1})$ by spherical polynomials of degree at most $j$. It is known that $\lambda:= (d-2)/2$ is the critical index for the summability of the Cesaro means on $H^1(S^{d-1})$. The main result of this paper states that, for $ f\in H^1(S^{d-1})$, $$\sum_{j=0}^N \f 1{j+1} \|\sigma_j^\lambda (f) -f\|_{H^1}\approx \sum_{j=0}^N \f 1{j+1} E_j(f, H^1),$$ where “$\approx$” means that the ratio of both sides lies between two positive constants independent of $f$ and $N$. 相似文献
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本文研究了紧致齐性空间上的Riesz位势算子与Bessel位势算子,Riesz变换与Bessel变换,给出了上述算子对应的核函数的具体构造并证明了Riesz变换与Bessel变换作为奇异积分算子的H ̄p有界性,p>0。 相似文献
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We show that the heat semigroup generated by certain perturbations of the Laplace–Beltrami operator on the Riemannian symmetric spaces of noncompact type is chaotic on their Lp-spaces when 2<p<∞. Both the range of p and the range of chaos-inducing perturbation are sharp. This extends a result of Ji and Weber [17] where it was shown that under identical conditions the heat operator is subspace-chaotic on these spaces. 相似文献
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《Journal of Functional Analysis》2023,284(6):109828
This paper is twofold. The first part aims to study the long-time asymptotic behavior of solutions to the heat equation on Riemannian symmetric spaces of noncompact type and of general rank. We show that any solution to the heat equation with bi-K-invariant initial data behaves asymptotically as the mass times the fundamental solution, and provide a counterexample in the non bi-K-invariant case. These answer problems recently raised by J.L. Vázquez. In the second part, we investigate the long-time asymptotic behavior of solutions to the heat equation associated with the so-called distinguished Laplacian on . Interestingly, we observe in this case phenomena which are similar to the Euclidean setting, namely asymptotic convergence with no bi-K-invariance condition and strong convergence. 相似文献
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We prove the almost everywhere convergence of the inverse spherical transform ofL
p
bi-K-invariant functions on the groupSL(2,R), 4/3<p≤2. The result appears to be sharp.
Partially supported by the MPI
Partially supported by the CMA 相似文献
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Gy. Gát 《Acta Mathematica Hungarica》2007,116(3):209-221
We prove the almost everywhere convergence of the Cesàro (C, α)-means of integrable functions σ
n
α
f → f for f ∈ L
1(I), where I is the group of 2-adic integers for every α > 0. This theorem for the case of α = 1 was proved by the author [1]. For the case of the (C, 1) Fejér means there are several generalizations known with respect to some orthonormal systems. One could mention the papers
[2, 9].
Research supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. T 048780. 相似文献
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本文首先引入Besel(Riesz)位势K¨othe函数空间Xs(Xs)的概念,然后讨论一类算子在Lebesgue-位势K¨othe函数空间Lq(-T,T;Xs)上的对偶估计.由此我们得到半群exp(it(-Δ)m/2)和算子A:=∫t0exp(i(t-τ)(-Δ)m/2)·dτ在Lebesgue-Besov空间Lq-T,T;·Bsp,2中的一些时间--空间Lp-Lp′估计.本文的系列文将给出这些估计的应用 相似文献
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Lars Diening 《Mathematische Nachrichten》2004,268(1):31-43
We study the Riesz potentials Iαf on the generalized Lebesgue spaces Lp(·)(?d), where 0 < α < d and Iαf(x) ? ∫equation/tex2gif-inf-3.gif |f(y)| |x – y|α – d dy. Under the assumptions that p locally satisfies |p(x) – p(x)| ≤ C/(– ln |x – y|) and is constant outside some large ball, we prove that Iα : Lp(·)(?d) → Lp?(·)(?d), where . If p is given only on a bounded domain Ω with Lipschitz boundary we show how to extend p to on ?d such that there exists a bounded linear extension operator ? : W1,p(·)(Ω) ? (?d), while the bounds and the continuity condition of p are preserved. As an application of Riesz potentials we prove the optimal Sobolev embeddings Wk,p(·)(?d) ?Lp*(·)(Rd) with and W1,p(·)(Ω) ? Lp*(·)(Ω) for k = 1. We show compactness of the embeddings W1,p(·)(Ω) ? Lq(·)(Ω), whenever q(x) ≤ p*(x) – ε for some ε > 0. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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对称链是一种特殊的偏序,用它已经得到了许多非常漂亮的结果.如果一个偏序集可以分解成不相交的对称链之并,则称此偏序集具有对称链分解.但目前已证明具有这种分解的偏序集并不多.L(m,n)={(x1,x2,…,xn)|xi均为整数且0≤x1≤x2≤…≤xm≤n},序关系≤定义为:X=(x1,x2,…,xm< 相似文献
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Zvonimir Janko 《组合设计杂志》1999,7(1):17-19
The existence of symmetric designs with parameters (105, 40, 15) was shown. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 17–19, 1999 相似文献
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LIU Weijun DAI Shaojun & GONG Luozhong School of Mathematics Central South University Changsha China Department of Mathematics Hunan University of Science Engineering Yongzhou China 《中国科学A辑(英文版)》2006,49(12)
After the classification of flag-transitive linear spaces, attention has now turned to line-transitive linear spaces. Such spaces are first divided into the point-imprimitive and the point-primitive, the first class is usually easy by the theorem of Delandtsheer and Doyen. The primitive ones are now subdivided, according to the O'Nan-Scotte theorem and some further work by Camina, into the socles which are an elementary abelian or non-abelian simple. In this paper, we consider the latter. Namely, T≤G≤Aut(T) and G acts line-transitively on finite linear spaces, where T is a non-abelian simple. We obtain some useful lemmas. In particular, we prove that when T is isomorphic to 3D4(q), then T is line-transitive, where q is a power of the prime p. 相似文献