共查询到20条相似文献,搜索用时 15 毫秒
1.
《数学物理学报(A辑)》2010,(6)
利用鞅变换,刻画了鞅Hardy空间与Hardy-Orlicz空间之间的相互关系:当p_Φ+∞时,证明了Hardy-Orlicz空间H_Φ~s中的鞅是Hardy空间H_1~s中的鞅变换;反之,H_1~s中的鞅也是H_Φ~s中的鞅变换.所得结果推广了已有文献中的相应结论. 相似文献
2.
Shangquan BU 《数学年刊B辑(英文版)》2011,32(2):293-302
The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H
p
($
\mathbb{T}
$
\mathbb{T}
d
;X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property (α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of
sets of bounded linear operators. It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property (α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. 相似文献
3.
Björn G. Walther 《Journal of Fourier Analysis and Applications》2014,20(6):1328-1337
Let \({\mathcal {F}}f\) be an abolutely convergent Fourier transform on the real line. We extend the following result of K. Karlander to \({\mathbf {R}^{n}}\) for \(n \ge 1\) : Any closed reflexive subspace \(\{ {\mathcal {F}}f \}\) of the space of continuous functions vanishing at infinity is of finite dimension. 相似文献
4.
Jonatan Lenells 《Studies in Applied Mathematics》2016,136(1):3-63
The unified transform method introduced by Fokas can be used to analyze initial‐boundary value problems for integrable evolution equations. The method involves several steps, including the definition of spectral functions via nonlinear Fourier transforms and the formulation of a Riemann‐Hilbert problem. We provide a rigorous implementation of these steps in the case of the mKdV equation in the quarter plane under limited regularity and decay assumptions. We give detailed estimates for the relevant nonlinear Fourier transforms. Using the theory of L2‐RH problems, we consider the construction of quarter plane solutions which are C1 in time and C3 in space. 相似文献
5.
Ferenc Weisz 《分析论及其应用》2001,17(2):32-44
It is proved that the maximal operator of the Marczinkiewicz-Fejér meams of a double Walsh-Fourier series is bounded from the two-dimensional dyadic martingale Hardy space H p to L p (2/3<p<∞) and is of weak type (1,1). As a consequence we obtain that the Marczinkiewicz-Fejér means of a function f∈L 1 converge a.e. to the function in question. Moreover, we prove that these means are uniformly bounded on H p whenever 2/3<p<∞. Thus, in case f∈H p , the Marczinkiewicz-Fejér means conv f in H p norm. The same results are proved for the conjugate means, too. 相似文献
6.
Ferenc Weisz 《逼近论及其应用》2001,17(2):32-44
It is proved that the maximal operator of the Marczinkiewicz-Fejér meams of a double Walsh-Fourier series is bounded from the two-dimensional dyadic martingale Hardy space H
p
to L
p (2/3<p<) and is of weak type (1,1). As a consequence we obtain that the Marczinkiewicz-Fejér means of a function fL
1
converge a.e. to the function in question. Moreover, we prove that these means are uniformly bounded on H
p
whenever 2/3<p<. Thus, in case fH
p
, the Marczinkiewicz-Fejér means conv f in H
p
norm. The same results are proved for the conjugate means, too. 相似文献
7.
Journal of Fourier Analysis and Applications - Let f be an element of the subspace $$(L^{q},l^{p})^{\alpha }({\mathbb {R}}^d)$$ ( $$1\le q \le \alpha \le p \le 2 $$ ) of the Wiener amalgam space... 相似文献
8.
Ferenc Mricz 《Mathematische Nachrichten》2000,219(1):163-180
We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L1 or the real Hardy spaces defined on ℝn, where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H1(ℝ) into L1(ℝ) and from L1(ℝ) into weak –L1(ℝ). We also prove that the double maximal Riemann operator is bounded from the hybrid Hardy spaces H(1,0)(ℝIsup2), H(0,1)(ℝ2) into weak –L1(ℝ2). Hence pointwise Riemann summability of Fourier integrals of functions in H(1,0) ∪ H(0,1)(ℝ2) follows almost everywhere.The maximal conjugate Riemann operators as well as the pointwise convergence of the conjugate Riemann means are also dealt with. 相似文献
9.
10.
Yong DING Shan Zhen LU Qing Ying XUE 《数学学报(英文版)》2007,23(9):1537-1552
In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 (R^n) to L1 (R^n) and from the weak Hardy space H^1,∞ (R^n) to L^1,∞ (R^n), respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and (1, 1) and of type (p,p) for 1 〈 p 〈 2, respectively extension of some known results. 相似文献
11.
Mathematical Notes - The question of the representability of a continuous function on $$\mathbb R^d$$ in the form of the Fourier integral of a finite Borel complex-valued measure on $$\mathbb R^d$$... 相似文献
12.
陈萱 《数学物理学报(A辑)》2021,(1):46-62
令L=?ΔHn+V是Heisenberg群Hn上Schr?dinger算子,其中非负位势V属于逆H?lder类.该文用分子刻画与L相关的Hardy型空间HL^p(H^n),进而得到了与L相关的Riesz变换的HL^p-有界性. 相似文献
13.
14.
Paula Cerejeiras Uwe Kähler Min Ku Frank Sommen 《Journal of Fourier Analysis and Applications》2014,20(4):715-750
We study the boundary behavior of discrete monogenic functions, i.e. null-solutions of a discrete Dirac operator, in the upper and lower half space. Calculating the Fourier symbol of the boundary operator we construct the corresponding discrete Hilbert transforms, the projection operators arising from them, and discuss the notion of discrete Hardy spaces. Hereby, we focus on the 3D-case with the generalization to the n-dimensional case being straightforward. 相似文献
15.
In this paper we investigate the convolution Hankel transforms on the Zemanian spaces of Hankel transformable functions and distributions. The convolution Hankel transform is defined on generalized functions by using the adjoint method. Our new definition includes as special cases other known definitions of the convolution Hankel transform of distributions. Finally we establish a distributional inversion formula for the transformation under consideration involving Bessel differential operators. 相似文献
16.
Remarks on Herz-Type Hardy Spaces 总被引:4,自引:0,他引:4
Akihiko Miyachi 《数学学报(英文版)》2001,17(2):339-360
Basic properties of the Herz-type Hardy spaces
, such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense
subspaces, etc., are established in the full range 0 < q < ∞.
Partly supported by the Grants-in-Aid for Scientific Research (A)(1)11304009, (B)(1)10440046, Japan Society
for the Promotion of Science. 相似文献
17.
Jacek Dziubański 《Journal of Geometric Analysis》2016,26(4):2639-2663
We characterize the Hardy space \(H^1\) in the rational Dunkl setting associated with the reflection group \(\mathbb {Z}_2^n\) by means of special Riesz transforms. As a corollary we obtain Riesz transforms characterization of \(H^1\) for product of Bessel operators in \((0,\infty )^n\). 相似文献
18.
Analysis Mathematica - In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces Hp and dyadic homogeneous Banach spaces X. Namely,... 相似文献
19.
Jingxuan Fang & Jiman Zhao 《分析论及其应用》2016,32(3):242-271
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators. 相似文献
20.
Sebastian Król 《Archiv der Mathematik》2016,106(5):457-470
We provide a variant of Hytönen’s embedding theorem, which allows us to extend and unify several sufficient conditions for a function to be a Fourier multiplier on the real Hardy spaces. 相似文献