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1.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2000,6(4):389-401
The two-parameter dyadic martingale Hardy spacesH
p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series
is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H
1
#
, L1), where the Hardy space H
1
#
is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H
1
#
converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too. 相似文献
2.
We show by example that the classical characterization of the Fourier series of periodic functions in Lp, 1<p≤+∞, as those trigonometric series whose Abel or Fejér means are uniformly bounded in Lp does not hold for general (non-periodic) trigonometric series in relation to Stepanov-almost-periodic functions, but that
it does hold under the additional hypothesis that the means are translation equicontinuous. We exhibit a bounded, infinitely
differentiable function that belongs to every class of Besicovitch-almost-periodic functions but is not equivalent in the
metric of Besicovitch-almost-periodic functions to any Stepanov-almost-periodic function. 相似文献
3.
H. Aleksanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2012,47(2):86-96
We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions
are found for system’s normalization to guarantee almost everywhere convergence, and convergence in L
p
(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees
convergence almost everywhere for functions from L
1(T), or uniform convergence for continuous functions. 相似文献
4.
If ψ ∈ L2(R), Λ is a discrete subset of the affine groupA =R
+ ×R, and w: Λ →R
+ is a weight function, then the weighted wavelet system generated by ψ, Λ, and w is
. In this article we define lower and upper weighted densities D
w
−
(Λ) and D
w
+
(Λ) of Λ with respect to the geometry of the affine group, and prove that there exist necessary conditions on a weighted wavelet
system in order that it possesses frame bounds. Specifically, we prove that if W(ψ, Λ, w) possesses an upper frame bound,
then the upper weighted density is finite. Furthermore, for the unweighted case w = 1, we prove that if W(ψ, Λ, 1) possesses
a lower frame bound and D
w
+
(Λ−1) < ∞, then the lower density is strictly positive. We apply these results to oversampled affine systems (which include the
classical affine and the quasi-affine systems as special cases), to co-affine wavelet systems, and to systems consisting only
of dilations, obtaining some new results relating density to the frame properties of these systems. 相似文献
5.
Let Γ be a regular curve and Lp(Γ),1<p<+∞, be the class of all complex-valued functions f defined on Γ which are such that |f|p is integrable in sense of Lebesgue. In this work, we define the kth p-Faber polynomial Fk.p(z), the kth p-Faber principle part ≈Fk.p(1/z) for Γ, and defined the nth p-Faber-Laurent rational function Rn,p(f, z) and p-generalized modulus of continuity Ωp of a function f of Lp(Γ). We investigate some properties of Fk.p(z) and ≈Fk.p(1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ωp in the mean of functions of Lp(Γ) by the rational functions Rn.p(.,z). 相似文献
6.
Abraham Neyman 《Israel Journal of Mathematics》1984,48(2-3):129-138
For fixed 1≦p<∞ theL
p-semi-norms onR
n
are identified with positive linear functionals on the closed linear subspace ofC(R
n
) spanned by the functions |<ξ, ·>|
p
, ξ∈R
n
. For every positive linear functional σ, on that space, the function Φσ:R
n
→R given by Φσ is anL
p-semi-norm and the mapping σ→Φσ is 1-1 and onto. The closed linear span of |<ξ, ·>|
p
, ξ∈R
n
is the space of all even continuous functions that are homogeneous of degreep, ifp is not an even integer and is the space of all homogeneous polynomials of degreep whenp is an even integer. This representation is used to prove that there is no finite list of norm inequalities that characterizes
linear isometric embeddability, in anyL
p unlessp=2.
Supported by the National Science Foundation MCS-79-06634 at U.C. Berkeley. 相似文献
7.
Suppose thatf is an element ofL
2(R
n
) whose orbit under the action ofSO(n) spans a finite-dimensional subspace. Then the spherical partial sums of the inverse Fourier transform off converge almost everywhere. 相似文献
8.
Harri Ojanen 《Journal of Fourier Analysis and Applications》2000,6(4):427-436
Weighted Lp estimates (1<p<∞) are shown for oscillatory singular integral operators with polynomial phase and a rough kernel of the form
eiP(x,y)Ω(x−y)h(|x−y|)|x−y|−n. We assume that Ω∈L logL(Sn−1) is homogeneous of degree zero and ∫Sn-1Ω=0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. 相似文献
9.
A Gabor frame multiplier is a bounded operator that maps normalized tight Gabor frame generators to normalized tight Gabor
frame generators. While characterization of such operators is still unknown, we give a complete characterization for the functional
Gabor frame multipliers. We prove that a L∞ -function h is a functional Gabor frame multiplier (for the time-frequency lattice aℤ × bℤ) if and only if it is unimodular
and
is a-periodic. Along the same line, we also characterize all the Gabor frame generators g (resp. frame wavelets ψ) for which
there is a function ∈ L∞(ℝ) such that {wgmn} (resp. ωψk,ℝ) is a normalized tight frame. 相似文献
10.
Zhu Xuexian 《分析论及其应用》1989,5(3):83-92
We show that if K(x,y)=Ω(x,y)/|x|n|y|m is a Calder n-Zygmund kerned on Rn×Rm, where Ω∈L2(Sn−1×Sm−1) and b(x,y) is any bounded function which is radial with x∈Rn and y∈Rm respectively, then b(x,y)K(x,y) is the kernel of a convolution operator which is bounded on Lp(Rn×Rm) for 1<p<∞ and n≧2, m≧2.
Project supported by NSFC 相似文献
11.
Let P be a non-negative, self-adjoint differential operator of degree d on ℝn. Assume that the associated Bochner-Riesz kernel s
R
δ
satisfies the estimate, |s
R
δ
(x, y)| ≤ C Rn/d(1+R1/d|x - y|-αδ+β)for some fixed constants a>0 and β. We study Lp boundedness of operators of the form m(P), m coming from the symbol class S
p
−α
. We prove that m(P) is bounded on LP if
. We also study multipliers associated to the Hermite operator H on ℝn and the special Hermite operator L on ℂn given by the symbols
. As a special case we obtain Lp boundedness of solutions to the Wave equation associated to H and L. 相似文献
12.
Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate analytic
semigroups of linear operators onL
p(R
n
), 1≦p≦∞. An explicit characterization of the domain is given for 1<p<∞. An application to parabolic problems is also included.
This work has been partially supported by the Research Funds of the Ministero della Pubblica Istruzione.
The authors are members of GNAFA (Consiglio Nazionale delle Ricerche). 相似文献
13.
In this paper, we consider the HKp(Rn) (1<p<∞) boundedness for certain oscillatory singular integral operators. 相似文献
14.
Patrik Wahlberg 《Integral Equations and Operator Theory》2007,59(1):99-128
We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators,
for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the
theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the
Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially
works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued
theory on continuity on certain modulation spaces when the symbol belongs to an Lp,q space and M∞, respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert
space as range space. 相似文献
15.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
16.
Marcinkiewicz Integrals with Non-Doubling Measures 总被引:2,自引:0,他引:2
Let μ be a positive Radon measure on
which may be non doubling. The only condition that μ must satisfy is μ(B(x, r)) ≤ Cr
n
for all
, r > 0 and some fixed constants C > 0 and n ∈ (0, d]. In this paper, we introduce the Marcinkiewicz integral related to a such measure with kernel satisfying some H?rmander-type
condition, and assume that it is bounded on L
2(μ). We then establish its boundedness, respectively, from the Lebesgue space L
1(μ) to the weak Lebesgue space L
1,∞(μ), from the Hardy space H
1(μ) to L
1(μ) and from the Lebesgue space L
∞(μ) to the space RBLO(μ). As a corollary, we obtain the boundedness of the Marcinkiewicz integral in the Lebesgue space L
p
(μ) with p ∈ (1,∞). Moreover, we establish the boundedness of the commutator generated by the RBMO(μ) function and the Marcinkiewicz integral with kernel satisfying certain slightly stronger H?rmander-type condition, respectively,
from L
p
(μ) with p ∈ (1,∞) to itself, from the space L log L(μ) to L
1,∞(μ) and from H
1(μ) to L
1,∞(μ). Some of the results are also new even for the classical Marcinkiewicz integral.
The third (corresponding) author was supported by National Science Foundation for Distinguished Young Scholars (No. 10425106)
and NCET (No. 04-0142) of China. 相似文献
17.
Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) −1). We derive a fast algorithm to compute the coefficients. 相似文献
18.
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
19.
Let T be a Calderón-Zygmund operator in a “non-homogeneous” space (
, d, μ), where, in particular, the measure μ may be non-doubling. Much of the classical theory of singular integrals has been
recently extended to this context by F. Nazarov, S. Treil, and A. Volberg and, independently by X. Tolsa. In the present work
we study some weighted inequalities for T*, which is the supremum of the truncated operators associated with T. Specifically, for1<p<∞, we obtain sufficient conditions for the weight in one side, which guarantee that another weight exists in the other
side, so that the corresponding Lp weighted inequality holds for T*. The main tool to deal with this problem is the theory of vector-valued inequalities for T* and some related operators. We discuss it first by showing how these operators are connected to the general theory of vector-valued
Calderón-Zygmund operators in non-homogeneous spaces, developed in our previous paper [6]. For the Cauchy integral operator
C, which is the main example, we apply the two-weight inequalities for C* to characterize the existence of principal values for functions in weighted Lp. 相似文献
20.
SunYongzhong 《高校应用数学学报(英文版)》2001,16(3):290-296
Abstract. In this note the existence of a singular integral operator T acting on Lipo(R“) spacesis studied. Suppose 相似文献