共查询到20条相似文献,搜索用时 218 毫秒
1.
The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss–Weierstrass, Abel–Poisson, and Bochner–Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceBsp, p, 1<p<∞, 0<s<1, thenTmtf (x)−f(x)=ox(ts) a.e. ast→0+. 相似文献
2.
T.S. Quek 《Journal of Mathematical Analysis and Applications》1997,210(2):742
We extend the Littlewood–Paley theorem toLpw(G), whereGis a locally compact Vilenkin group andware weights satisfying the MuckenhouptApcondition. As an application we obtain a mixed-norm type multiplier result onLpw(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ L∞(Γ) to be a multiplier on the power weightedLpα(G) in terms of its smoothness condition. 相似文献
3.
We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π
′ of
GLm(\mathbbAF)GL_{m}(\mathbb{A}_{F})
and
GLm¢(\mathbbAF)GL_{m^{\prime }}(\mathbb{A}_{F})
. Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
attached to
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
. Then, we deduce a full asymptotic expansion of the archimedean contribution to
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial
zeros of
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
, the nth Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for
the archimedean Langlands parameters μ
π
(v,j) of π. Namely, we prove that under GRH for
L(s,pf×[(p)\tilde]f)L(s,\pi _{f}\times \widetilde{\pi}_{f})
one has
|Remp(v,j)| £ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4}
for all archimedean places v at which π is unramified and all j=1,…,m. 相似文献
4.
C. Carton-Lebrun 《Journal of Approximation Theory》1977,21(4):356-360
Let fεLp(R), gεLq(R) with 1<p<∞, 1<q<∞ and let Hf, Hg be their respective Hilbert transforms. We give a simple proof of the identity Hf · Hg − f · G = H(f · Hg + g · Hf) a.e. and of its inverse in the case (1/p) + (1/q) 1 which includes the cases already considered by Cossar and Tricomi. We next derive applications, especially to boundary values of analytic functions. 相似文献
5.
Helena Barbas 《Journal of Geometric Analysis》2010,20(1):1-38
The aim of this article is to prove the following theorem.
Theorem
Let
p
be in (1,∞), ℍ
n,m
a group of Heisenberg type, ℛ the vector of the Riesz transforms on ℍ
n,m
. There exists a constant
C
p
independent of
n
and
m
such that for every
f∈L
p
(ℍ
n,m
)
Cp-1e-0.45m||f||Lp(\mathbbHn,m) £ |||Rf|||Lp(\mathbbHn,m) £ Cpe0.45m||f||Lp(\mathbbHn,m).C_p^{-1}e^{-0.45m}\|f\|_{L^p(\mathbb{H}_{n,m})}\leq\||\mathcal{R}f|\|_{L^p(\mathbb{H}_{n,m})}\leq C_pe^{0.45m}\|f\|_{L^p(\mathbb{H}_{n,m})}. 相似文献
6.
Let Bn( f,q;x), n=1,2,… be q-Bernstein polynomials of a function f : [0,1]→C. The polynomials Bn( f,1;x) are classical Bernstein polynomials. For q≠1 the properties of q-Bernstein polynomials differ essentially from those in the classical case. This paper deals with approximating properties of q-Bernstein polynomials in the case q>1 with respect to both n and q. Some estimates on the rate of convergence are given. In particular, it is proved that for a function f analytic in {z: |z|<q+} the rate of convergence of {Bn( f,q;x)} to f(x) in the norm of C[0,1] has the order q−n (versus 1/n for the classical Bernstein polynomials). Also iterates of q-Bernstein polynomials {Bnjn( f,q;x)}, where both n→∞ and jn→∞, are studied. It is shown that for q(0,1) the asymptotic behavior of such iterates is quite different from the classical case. In particular, the limit does not depend on the rate of jn→∞. 相似文献
7.
We prove that for f ε E = C(G) or Lp(G), 1 p < ∞, where G is any compact connected Lie group, and for n 1, there is a trigonometric polynomial tn on G of degree n so that f − tnE Crωr(n−1,f). Here ωr(t, f) denotes the rth modulus of continuity of f. Using this and sharp estimates of the Lebesgue constants recently obtained by Giulini and Travaglini, we obtain “best possible” criteria for the norm convergence of the Fourier series of f. 相似文献
8.
For a functionfLp[−1, 1], 0<p<∞, with finitely many sign changes, we construct a sequence of polynomialsPnΠnwhich are copositive withfand such that f−PnpCω(f, (n+1)−1)p, whereω(f, t)pdenotes the Ditzian–Totik modulus of continuity inLpmetric. It was shown by S. P. Zhou that this estimate is exact in the sense that if f has at least one sign change, thenωcannot be replaced byω2if 1<p<∞. In fact, we show that even for positive approximation and all 0<p<∞ the same conclusion is true. Also, some results for (co)positive spline approximation, exact in the same sense, are obtained. 相似文献
9.
Harald Woracek 《Monatshefte für Mathematik》2012,33(3):105-149
A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ¥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L2(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D\mathfrakmDx{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as
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