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1.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained. 相似文献
2.
Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure. 相似文献
3.
Boundedness of commutators on Hardy type spaces 总被引:18,自引:0,他引:18
Let [b, T] be the commutator of the function b ∈ Lipβ(Rn) (0 <β≤ 1) and the CalderónZygmund singular integral operator T. The authors study the boundedness properties of [b, T] on the classical Hardy spaces and the Herz-type Hardy spaces in non-extreme cases. For the boundedness of these commutators in extreme cases, some characterizations are also given. Moreover, the authors prove that these commutators are bounded from Hardy type spaces to the weak Lebesgue or Herz spaces in extreme cases. 相似文献
4.
O. V. Pugachev 《Mathematical Notes》1999,65(3):315-325
We generalize the Airault-Malliavin theorem on the existence of surface measures on infinite-dimensional spaces with Gaussian
measures on surfaces. We prove that the sets of capacities generated by Sobolev classes on infinite-dimensional spaces are
dense.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 377–388, March, 1999. 相似文献
5.
Let ( Y,d,dl )\left( {\mathcal{Y},d,d\lambda } \right) be (ℝ
n
, |·|, μ), where |·| is the Euclidean distance, μ is a nonnegative Radon measure on ℝ
n
satisfying the polynomial growth condition, or the Gauss measure metric space (ℝ
n
, |·|, d
λ
), or the space (S, d, ρ), where S ≡ ℝ
n
⋉ ℝ+ is the (ax + b)-group, d is the left-invariant Riemannian metric and ρ is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces
{ Xs ( Y ) }0 < s \leqslant ¥\left\{ {X_s \left( \mathcal{Y} \right)} \right\}_{0 < s \leqslant \infty } and the BMO-type spaces
{ BMO( Y, s ) }0 < s \leqslant ¥\left\{ {BMO\left( {\mathcal{Y}, s} \right)} \right\}_{0 < s \leqslant \infty }. Let H
1
( Y )\left( \mathcal{Y} \right) be the known atomic Hardy space and L
01
( Y )\left( \mathcal{Y} \right) the subspace of f ∈ L
1
( Y )\left( \mathcal{Y} \right) with integral 0. The authors prove that the dual space of X
s
( Y )\left( \mathcal{Y} \right) is BMO( Y,s )BMO\left( {\mathcal{Y},s} \right) when s ∈ (0,∞), X
s
( Y )\left( \mathcal{Y} \right) = H
1
( Y )\left( \mathcal{Y} \right) when s ∈ (0, 1], and X
∞
( Y )\left( \mathcal{Y} \right) = L
01
( Y )\left( \mathcal{Y} \right) (or L
1
( Y )\left( \mathcal{Y} \right)). As applications, the authors show that if T is a linear operator bounded from H
1
( Y )\left( \mathcal{Y} \right) to L
1
( Y )\left( \mathcal{Y} \right) and from L
1
( Y )\left( \mathcal{Y} \right) to L
1,∞
( Y )\left( \mathcal{Y} \right), then for all r ∈ (1,∞) and s ∈ (r,∞], T is bounded from X
r
( Y )\left( \mathcal{Y} \right) to the Lorentz space L
1,s
( Y )\left( \mathcal{Y} \right), which applies to the Calderón-Zygmund operator on (ℝ
n
, |·|, μ), the imaginary powers of the Ornstein-Uhlenbeck operator on (ℝ
n
, |·|, d
γ
) and the spectral operator associated with the spectral multiplier on (S, d, ρ). All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces. 相似文献
6.
In this paper we introduce a new type of difference operator Δ
m
n
for fixed m, n ∈ ℕ. We define the sequence spaces ℓ∞(Δ
m
n
), c(Δ
m
n
) and c
0(Δ
m
n
) and study some topological properties of these spaces. We obtain some inclusion relations involving these sequence spaces.
These notions generalize many earlier existing notions on difference sequence spaces.
相似文献
7.
Vugar E. Ismailov 《Proceedings Mathematical Sciences》2009,119(1):45-52
Let X
1, …, X
n
be compact spaces and X = X
1 × … × X
n
. Consider the approximation of a function ƒ ∈ C(X) by sums g
1(x
1)+…+g
n
(x
n
), where g
i
∈ C(X
i
), i = 1, …, n. In [8], Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points
of X, called ‘projection cycles’. However, his proof had a gap, which was pointed out by Marshall and O’Farrell [15]. But the
question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb’s formula holds in a
stronger form. 相似文献
8.
In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces
and
, where ω1,ω3 ∈ A1-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study
the boundedness of some potential operators on these spaces.
Supported by the NNSF of China 相似文献
9.
Wen-ming Li Shan-zhen Lu Hui-xia Mo 《应用数学学报(英文版)》2007,23(1):113-122
Let[b,T]be the commutator generated by a Lipschitz function b ∈ Lip(β)(0<β<1)and multiplierT.The authors studied the boundedness of[b,T]on the Lebesgue spaces and Hardy spaces. 相似文献
10.
In this paper, the boundedness of an oscillating multiplier m γ,β for different β on the Herz type spaces is obtained. This operator was initially studied by Wainger and Fefferman-Stein. Our results extend one of the main results in a paper by Xiaochun Li and Shanzhen Lu for the non-weighted case, if β is close to 1 or α is suitably large. For β ≥ 1, the results with no weights on the Herz type spaces are also new. 相似文献
11.
12.
Let (X, d) be a compact metric space and let (X) denote the space of all finite signed Borel measures on X. Define I: (X) → ℝ by I(μ) = ∫
X
∫
X
d(x, y)dμ(x)dμ(y), and set M(X) = sup I(μ), where μ ranges over the collection of measures in (X) of total mass 1. The space (X, d) is quasihypermetric if I(μ) ≦ 0 for all measures μ in (X) of total mass 0 and is strictly quasihypermetric if in addition the equality I(μ) = 0 holds amongst measures μ of mass 0 only for the zero measure.
This paper explores the constant M(X) and other geometric aspects of X in the case when the space X is finite, focusing first on the significance of the maximal strictly quasihypermetric subspaces of a given finite quasihypermetric
space and second on the class of finite metric spaces which are L
1-embeddable. While most of the results are for finite spaces, several apply also in the general compact case. The analysis
builds upon earlier more general work of the authors [11] [13].
相似文献
13.
Boundedness of Some Maximal Commutators in Hardy-type Spaces with Non-doubling Measures 总被引:1,自引:0,他引:1
Guo En HU Yan MENG Da Chun YANG 《数学学报(英文版)》2007,23(6):1129-1148
Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO(μ) functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO(μ) functions, of the Hardv soace H^I(μ) of Tolsa. 相似文献
14.
Suppose μ is a Radon measure on ℝ
d
, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C0>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C0rn, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results
for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1
theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7]. 相似文献
15.
Yue XiukuiDept. of Math. Phys. Shandong Institute of Architecture Engineering Shandong China. 《高校应用数学学报(英文版)》2004,19(3):252-256
§1 IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0
相似文献
16.
Eiichi Nakai 《数学学报(英文版)》2008,24(8):1243-1268
Let X = (X, d,μ) The purpose of this paper is to be a space of homogeneous type in the sense of Coifman and Weiss. generalize the definition of Hardy space H^P(X) and prove that the generalized Hardy spaces have the same property as H^P(X). Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R^n case. Let (X, δ, μ) be the normalized space of (X, d, μ) in the sense of Macias and Segovia. We also study the relations of our function spaces for (X, d, μ) and (X, δ,μ). 相似文献
17.
Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x
k
): (ϕk(|x
k
|)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P
f
from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications
we consider superposition operators on some multiplier sequence spaces of Maddox type.
This research was supported by Estonian Science Foundation Grant 5376. 相似文献
18.
In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 <β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 <α≤ 1). 相似文献
19.
It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2
X
of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2
X
is homeomorphic to Π2 ifX is a Baire space, and toQ∖Π1 ifX contains a dense absoluteG
δ-setG ⊂X such that the intersectionG ∩U is connected for any open connectedU ⊂X. (Here Π1, Π1⊂X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective
classes.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997.
Translated by O. V. Sipacheva 相似文献
20.
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship
among some martingale spaces such asH
α(X) andρ
H
α in the case 0< α⩽ are studied. It is shown that there is a close connection between the results and the smoothness and convexity
of the value spaces.
Project supported by the National Natural Science Foundation of China (Grant No. 19771063). 相似文献