共查询到20条相似文献,搜索用时 603 毫秒
1.
Raquel Crescimbeni Francisco Javier Martín-Reyes Alberto De La Torre José L. Torrea 《数学学报(英文版)》2010,26(10):1827-1838
In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP(R, w(x)dx) into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞. 相似文献
2.
Let 0<p≤1<q<0, andw
1
,w
2
∈ A
1
(Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the
homogeneous weighted Herz-type Hardy spacesH Kα, p
q(w1; w2) to the homogeneous weighted Herz spacesK
α, p
q
(w1; w2), provided α=n(1−1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spacesH K
α, p
q
(w
1;w
2) is also investigated.
Supported by the National Natural Science Foundation of China 相似文献
3.
We prove a statement on the boundedness of a certain class of singular type operators in the weighted spaces with variable exponent p(x) and a power type weight w, from which we derive the boundedness of pseudodifferential operators of H?rmander class S
0
1,0 in such spaces.
This gives us a possibility to obtain a necessary and sufficient condition for pseudodifferential operators of the class OPS
m
1,0 with symbols slowly oscillating at infinity, to be Fredholm within the frameworks of weighted Sobolev spaces with constant smoothness s, variable p(·)-exponent, and exponential weights w.
Supported by CONACYT Project No.43432 (Mexico), the Project HAOTA of CEMAT at Instituto Superior Técnico, Lisbon (Portugal)
and the INTAS Project “Variable Exponent Analysis” Nr.06-1000017-8792. 相似文献
4.
In this article we define and investigate a local Hardy–Littlewood maximal operator in Euclidean spaces. It is proved that this operator satisfies weighted L p , p > 1, and weighted weak type (1,1) estimates with weight function ${w \in A^p_{\rm{loc}}}In this article we define and investigate a local Hardy–Littlewood maximal operator in Euclidean spaces. It is proved that
this operator satisfies weighted L
p
, p > 1, and weighted weak type (1,1) estimates with weight function w ? Aploc{w \in A^p_{\rm{loc}}}, the class of local A
p
weights which is larger than the Muckenhoupt A
p
class. Also, the condition w ? Aploc{w \in A^p_{\rm{loc}}} turns out to be necessary for the weighted weak type (p,p), p ≥ 1, inequality to hold. 相似文献
5.
V. Kokilashvili 《Journal of Mathematical Sciences》2010,170(1):20-33
Boundedness criteria for the Calderón singular integral, Riesz transform and Cauchy singular integral in generalized weighted
grand Lebesgue spaces L
p),θ
w
, 1 < p < ∞, are studied. It is shown that an operator K of this type is bounded in L
p),θ
w
if and only if the weight w satisfies the Muckenhoupt A
p
condition. Bibliography: 15 titles. 相似文献
6.
Thomas Kühn Hans-Gerd Leopold Winfried Sickel Leszek Skrzypczak 《Mathematische Zeitschrift》2007,255(1):1-15
We determine the exact asymptotic order of the entropy numbers of compact embeddings of weighted Besov spaces in the case where the ratio of the weights w(x) = w
1(x)/w
2(x) is of logarithmic type. This complements the known results for weights of polynomial type. The estimates are given in terms of the number 1/p = 1/p
1 − 1/p
2 and the function w(x). We find an interesting new effect: if the growth rate at infinity of w(x) is below a certain critical bound, then the entropy numbers depend only on w(x) and no longer on the parameters of the two Besov spaces. All results remain valid for Triebel–Lizorkin spaces as well. 相似文献
7.
We consider generalized Morrey type spaces Mp( ·),q( ·),w( ·)( W) {\mathcal{M}^{p\left( \cdot \right),\theta \left( \cdot \right),\omega \left( \cdot \right)}}\left( \Omega \right) with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets
W ì \mathbbRn \Omega \subset {\mathbb{R}^n} , we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular integral operators with
standard kernel. We prove a Sobolev–Adams type embedding theorem Mp( ·),q1( ·),w1( ·)( W) ? Mq( ·),q2( ·),w2( ·)( W) {\mathcal{M}^{p\left( \cdot \right),{\theta_1}\left( \cdot \right),{\omega_1}\left( \cdot \right)}}\left( \Omega \right) \to {\mathcal{M}^{q\left( \cdot \right),{\theta_2}\left( \cdot \right),{\omega_2}\left( \cdot \right)}}\left( \Omega \right) for the potential type operator I
α(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles. 相似文献
8.
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from H K αq ,p ( w1 ; w2 ) into Kαq ,p (w 1; w2). 相似文献
9.
Shuichi Sato 《Journal of Mathematical Analysis and Applications》2003,278(2):308-323
We prove some weighted estimates for certain Littlewood-Paley operators on the weighted Hardy spaces Hwp (0<p?1) and on the weighted Lp spaces. We also prove some weighted estimates for the Bochner-Riesz operators and the spherical means. 相似文献
10.
The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces
L
p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential
operators on the spaces
Lp(·)(\mathbbR +,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting
on L
p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential
operators on
\mathbbR+{\mathbb{R}_{+}} and local invertibility of singular integral operators on
\mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L
p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities. 相似文献
11.
Anders Björn 《Czechoslovak Mathematical Journal》2006,56(1):179-227
We develop a theory of removable singularities for the weighted Bergman space
, where μ is a Radon measure on ℂ. The set A is weakly removable for
, and strongly removable for
.
The general theory developed is in many ways similar to the theory of removable singularities for Hardy H
p
spaces, BMO and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible
properties, e.g. the union of two compact removable singularities needs not be removable.
In the case when weak and strong removability are the same for all sets, in particular if μ is absolutely continuous with respect to the Lebesgue measure m, we are able to say more than in the general case. In this case we obtain a Dolzhenko type result saying that a countable
union of compact removable singularities is removable.
When dμ = wdm and w is a Muckenhoupt A
p
weight, 1 < p < ∞, the removable singularities are characterized as the null sets of the weighted Sobolev space capacity with respect to
the dual exponent p′ = p/(p − 1) and the dual weight w′ = w
1/(1 − p). 相似文献
12.
Summary We prove a Schur test for mixed-norm spaces Lp,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces lp,q w, 1 < p,q < ∞, and wis a weight. We show that if w 1, and w 2are two weight functions on the index sets Jx Iand K x Lrespectively, and A =(a ji, kl ) j∈J, i∈I, k∈K, l∈L is an infinite matrix, then under certain conditions, Ais a bounded operator from lp,q w1, 1 < p,q < ∞ to lp,q w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.</o:p> 相似文献
13.
Zhuo Ping Ruan 《数学学报(英文版)》2011,27(10):1967-1978
We apply discrete Littlewood-Paley-Stein theory, developed by Han and Lu, to establish Calderón-Zygmund decompositions and
interpolation theorems on weighted Hardy spaces H
w
p
for ω ∈ A
∞ in both the one-parameter and two-parameter cases. 相似文献
14.
Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent 总被引:1,自引:0,他引:1
We prove the boundedness of the maximal operator Mr in the spaces L^p(·)(Г,p) with variable exponent p(t) and power weight p on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Г. We prove also weighted Sobolev type L^p(·)(Г, p) → L^q(·)(Г, p)-theorem for potential operators on Carleson curves. 相似文献
15.
Maria De Natividade 《Monatshefte für Mathematik》2011,164(1):87-114
Democracy functions of wavelet admissible bases are computed for weighted Orlicz Spaces L ??(w) in terms of the fundamental function of L ??(w). In particular, we prove that these bases are greedy in L ??(w) if and only if L ??(w) =?L p (w), 1?<?p?<???. Also, sharp embeddings for the approximation spaces are given in terms of weighted discrete Lorentz spaces. For L p (w) the approximation spaces are identified with weighted Besov spaces. 相似文献
16.
We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functionsH
ν
p
∞ when the symbolφ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch
type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.
The research of the second author was partially supported by the Academy of Finland Project No. 51906; the research of this
paper was carried out while this author was visiting Kent State University, whose hospitality is acknowledged with thanks. 相似文献
17.
We prove that every compact nilpotent ring R of characteristic p > 0 can be embedded in a ring of upper triangular matrices over a compact commutative ring. Furthermore, we prove that every
compact topologically nilpotent ring R of characteristic p > 0, is embedded in a ring of infinite triangular matrices over
\mathbbFpw(R)\mathbb{F}_{p}^{w(R)}. 相似文献
18.
O. V. Besov 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):25-45
On an irregular domain G ⊂ ℝ
n
of a certain type, we introduce spaces of functions of fractional smoothness s > 0. We prove embedding theorems relating these spaces to the Sobolev spaces W
p
m
(G) and Lebesgue spaces L
p
(G). 相似文献
19.
An elementary proof of the (known) fact that each element of the Banach spaceℓ
w
p
(X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ
w
p
(X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications
to spaces of compact operators on Banach sequence spaces are considered. 相似文献
20.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces
Lw2(\mathbbR){L_{\omega}^{2}(\mathbb{R})} For operators M in the algebra generated by the convolutions with
f ? Cc(\mathbb R){\phi \in {C_c(\mathbb {R})}} we show that [`(m(W))] = s(M){\overline{\mu(\Omega)} = \sigma(M)}, where the set Ω is determined by the spectrum of the shift S and μ is the symbol of M. For the general multipliers M we establish that [`(m(W))]{\overline{\mu(\Omega)}} is included in σ(M). A generalization of these results is given for the weighted spaces
L2w(\mathbb Rk){L^2_{\omega}(\mathbb {R}^{k})} where the weight ω has a special form. 相似文献