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1.
Let \(X_1\) and \(X_2\) be metric spaces equipped with doubling measures and let \(L_1\) and \(L_2\) be nonnegative self-adjoint operators acting on \(L^2(X_1)\) and \(L^2(X_2)\) respectively. We study multivariable spectral multipliers \(F(L_1, L_2)\) acting on the Cartesian product of \(X_1\) and \(X_2\). Under the assumptions of the finite propagation speed property and Plancherel or Stein–Tomas restriction type estimates on the operators \(L_1\) and \(L_2\), we show that if a function F satisfies a Marcinkiewicz-type differential condition then the spectral multiplier operator \(F(L_1, L_2)\) is bounded from appropriate Hardy spaces to Lebesgue spaces on the product space \(X_1\times X_2\). We apply our results to the analysis of second-order elliptic operators in the product setting, specifically Riesz-transform-like operators and double Bochner–Riesz means. 相似文献
2.
In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained. 相似文献
3.
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
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6.
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
7.
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
8.
In this paper, we study the boundedness of the Hausdorff operator H_? on the real line R. First, we start with an easy case by establishing the boundedness of the Hausdorff operator on the Lebesgue space L~p(R)and the Hardy space H~1(R). The key idea is to reformulate H_? as a Calder′on-Zygmund convolution operator,from which its boundedness is proved by verifying the Hrmander condition of the convolution kernel. Secondly,to prove the boundedness on the Hardy space H~p(R) with 0 p 1, we rewrite the Hausdorff operator as a singular integral operator with the non-convolution kernel. This novel reformulation, in combination with the Taibleson-Weiss molecular characterization of H~p(R) spaces, enables us to obtain the desired results. Those results significantly extend the known boundedness of the Hausdorff operator on H~1(R). 相似文献
9.
Mathematical Notes - It is known that the boundedness of the composition operator on Lebesgue spaces is equivalent to the integrability of the volume derivative of the measurable mapping inducing... 相似文献
10.
In this paper, we study the structure of the Hardy space Hpb{H^p_b} associated with a para-accretive function b, which was introduced in Han et al. (J. Geom. Anal. 14:291–318, 2004). The main result is to establish a new atomic decomposition of Hpb{H^p_b} . As applications, we obtain criterions for the boundedness of operators on Hpb{H^p_b} and a characterization of the dual space of Hpb{H^p_b} . The classification of Hpb{H^p_b} and Calderón–Zygmund decomposition are also discussed. 相似文献
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J. Hounie Rafael Augusto dos Santos Kapp 《Journal of Fourier Analysis and Applications》2009,15(2):153-178
In this work, we study the continuity of pseudodifferential operators on local Hardy spaces h
p
(ℝ
n
) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S
1,δ
0(ℝ
n
), 0≤δ<1, and in some subclasses of S
1,10(ℝ
n
) are bounded on h
p
(ℝ
n
) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂
t
+ib(x,t)∂
x
, b(x,t)≥0, in spaces of mixed norm involving Hardy spaces.
Work supported in part by CNPq, FINEP, and FAPESP. 相似文献
14.
We establish the connection between the boundedness of convolution operators on Hp(ℝN) and some related operators on Hp(ℤN). The results we obtain here extend the already known for Lp spaces with p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential type belonging to Hardy spaces 相似文献
15.
In this paper we introduce and study the anisotropic local Hardy spaces
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}) 0<p≤1, associated with the expansive matrix A. We obtain an atomic characterization of the distributions in
hAp(\mathbbRn)h_{A}^{p}(\mathbb{R}^{n}). Also we describe the dual spaces of our local Hardy anisotropic spaces as anisotropic Campanato type spaces. 相似文献
16.
We introduce and explore Hardy spaces defined by mixed Lebesgue norms and anisotropic dilations. We prove that the definitions of these spaces in terms of smooth, non-tangential, auxiliary, grand, and Poisson maximal operators coincide. We also study the relation between anisotropic mixed-norm Hardy spaces and mixed-norm Lebesgue spaces. 相似文献
17.
Hardy空间上的有界复合算子 总被引:2,自引:0,他引:2
本文讨论了由解析映射φ:Bn→Bm诱导复合算子的有界性;特别地,研究了由保测内映射诱导复合算子的性质.作为推论,得到了W.Rudin[10]中一个公开问题的解答. 相似文献
18.
In this paper, we investigate the properties on some classes of complex-valued functions which satisfy certain elliptic equations. First, we discuss the Lipschitz-type spaces and Hardy spaces on these functions, and then we show that for a class of complex-valued functions, if it admits some bounded Dirichlet-type energy integral, then it has a harmonic majorant in the unit disk. 相似文献
19.
Global solvability and asymptotics of semilinear parabolic Cauchy problems in n are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over n, n . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed. 相似文献
20.
We establish rather weak conditions on
under which the small scale
affine system
spans
.
The conditions are that the periodization of |ψ| be locally in Lp, that
, and
that the dilation matrices aj are expanding, meaning
. The periodization
of ψ need not be constant; that is, the integer translates
need not form a partition of unity.
The proof involves explicitly approximating an arbitrary function f using a linear combination
of the
, with the coefficients in the linear combination being local average values
of f . 相似文献