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José María Martell 《Journal of Mathematical Analysis and Applications》2004,294(1):223-236
We prove two-weight, weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type. We show that the operators in question are bounded from Lp(v) to Lq,∞(u), 1<p?q<∞, provided the pair of weights (u,v) verifies a Muckenhoupt condition with a “power-bump” on the weight u. 相似文献
3.
利用单边权的外推法,本文得到了由单边算子与Lipschitz函数生成的交换子的加权有界性质,而且给出了判定两类单边极大算子交换子有界性的充分必要条件. 相似文献
4.
Considering time-periodic Stokes flow around a rotating body in or we prove weighted a priori estimates in L
q
-spaces for the whole space problem. After a time-dependent change of coordinates the problem is reduced to a stationary Stokes
equation with the additional term in the equation of momentum, where ω denotes the angular velocity. In cylindrical coordinates attached to the rotating body we allow for Muckenhoupt weights which
may be anisotropic or even depend on the angular variable and prove weighted L
q
-estimates using the weighted theory of Littlewood-Paley decomposition and of maximal operators.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan no. AV0Z10190503,
by the Grant Agency of the Academy of Sciences No. IAA100190505, and by the joint research project of DAAD (D/04/25763) and
the Academy of Sciences of the Czech Republic (D-CZ 3/05-06). 相似文献
5.
《Indagationes Mathematicae》2022,33(2):397-420
In a previous paper, we obtained several “compact versions” of Rubio de Francia’s weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calderón–Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Fréchet–Kolmogorov criterion of compactness, whereas we avoid this by relying on “softer” tools, which might have an independent interest in view of further extensions of the method. 相似文献
6.
We give a characterization of the weights u(·) and v(·) for which the fractional maximal operator M
s is bounded from the weighted Lebesgue spaces L
p(l
r, vdx) into L
q(l
r, udx) whenever 0 s < n, 1 < p, r < , and 1 q < . 相似文献
7.
In this paper, we consider weighted norm inequalities for fractional maximal operators and fractional integral operators. For suitable weights, we prove the two-weight norm inequalities for both operators on weighted Morrey spaces. 相似文献
8.
Filipe Dantas 《Mathematical Methods in the Applied Sciences》2019,42(5):1572-1587
This work deals with the study of maximal ?p‐regularity of a pair (A,B) of bounded linear operators on a complex Banach space associated to the second order difference equation un + 2 = Bun + 1 + Aun + fn, where f is a given sequence on . We obtain results of characterization based on spectral analysis of the discrete sine family, which is the resolvent family of this equation. 相似文献
9.
In this paper,we study the weighted estimates for multilinear pseudodifferential operators.We show that a multilinear pseudodifferential operator is bounded with respect to multiple weights whenever its symbol satisfies some smoothness and decay conditions.Our result generalizes similar ones from the classical Ap weights to multiple weights. 相似文献
10.
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
11.
M. W. Wong 《Mathematische Nachrichten》2006,279(3):319-326
We construct the minimal and maximal extensions in L p (?n ), 1 < p < ∞, for M ‐elliptic pseudo‐differential operators initiated by Garello and Morando. We prove that they are equal and determine the domains of the minimal, and hence maximal, extensions of M ‐elliptic pseudo‐differential operators. For M ‐elliptic pseudodifferential operators with constant coefficients, the spectra and essential spectra are computed. An application to quantization is given. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
In this work we give extrapolation results on weighted Lebesgue spaces for weights associated to a family of operators. The starting point for the extrapolation can be the knowledge of boundedness on a particular Lebesgue space as well as the boundedness on the extremal case L ∞. This analysis can be applied to a variety of operators appearing in the context of a Schrödinger operator (??Δ?+?V) where V satisfies a reverse Hölder inequality. In that case the weights involved are a localized version of Muckenhoupt weights. 相似文献
13.
Viorel Catană 《Applicable analysis》2013,92(6):657-666
Following Wong's point of view, we construct the minimal and maximal extension in Lp (? n ), 1 < p < ∞ for M-hypoelliptic pseudo-differential operators, which have been introduced and studied by Garello and Morando. We give some facts about the domain of minimal and maximal extensions of M-hypoelliptic pseudo-differential operators. For M-hypoelliptic pseudo-differential operators with constant coefficients, the spectrum and essential spectrum are computed. 相似文献
14.
The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity 总被引:1,自引:0,他引:1
Andreas Fr?hlich 《Mathematische Annalen》2007,339(2):287-316
In this paper we establish a general weighted L
q
-theory of the Stokes operator in the whole space, the half space and a bounded domain for general Muckenhoupt weights . We show weighted L
q
-estimates for the Stokes resolvent system in bounded domains for general Muckenhoupt weights. These weighted resolvent estimates
imply not only that the Stokes operator generates a bounded analytic semigroup but even yield the maximal L
p
-regularity of in the respective weighted L
q
-spaces for arbitrary Muckenhoupt weights . This conclusion is archived by combining a recent characterisation of maximal L
p
-regularity by -bounded families due to Weis [Operator-valued Fourier multiplier theorems and maximal L
p
-regularity. Preprint (1999)] with the fact that for L
q
-spaces -boundedness is implied by weighted estimates. 相似文献
15.
We show that the Poisson maximal operator for the tube over the light-cone, P
*, is bounded in the weighted space L
p
(w) if and only if the weight w(x) belongs to the Muckenhoupt class A
p
. We also characterize with a geometric condition related to the intrinsic geometry of the cone the weights v(x) for which P
* is bounded from L
p
(v) into L
p
(u), for some other weight u(x) > 0. Some applications to a.e. restricted convergence of Poisson integrals are given. 相似文献
16.
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calderón-Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators. 相似文献
17.
Elona Agora María J. Carro Javier Soria 《Journal of Fourier Analysis and Applications》2013,19(4):712-730
We characterize the weak-type boundedness of the Hilbert transform H on weighted Lorentz spaces $\varLambda^{p}_{u}(w)$ , with p>0, in terms of some geometric conditions on the weights u and w and the weak-type boundedness of the Hardy–Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of H on weighted Lebesgue spaces L p (u) and Muckenhoupt weights A p , and the theory on classical Lorentz spaces Λ p (w) and Ariño-Muckenhoupt weights B p . 相似文献
18.
Ramazan Akgün 《复变函数与椭圆型方程》2019,64(2):330-351
Mixed modulus of smoothness in weighted Lebesgue spaces with Muckenhoupt weights are investigated. Using mixed modulus of smoothness we obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. Also we obtain equivalences between mixed modulus of smoothness and K-functional and realization functional. Fractional order modulus of smoothness is considered as well. 相似文献
19.
《Expositiones Mathematicae》2022,40(1):23-44
In this paper, weighted extra-weak and weak type inequalities have been characterized for the one-sided Hardy–Littlewood maximal function on the plane. We have addressed conditions on pair of weights for which the dyadic one-sided maximal function on higher dimension is locally integrable. In the process, we characterize weights for which the one-sided Hardy-Littlewood maximal function satisfies restricted weak type inequalities on the plane, thus extending the result of Kerman and Torchinsky to the one-sided Hardy-Littlewood maximal function. 相似文献
20.
Bruno Bongioanni Adrián Cabral Eleonor Harboure 《Mathematische Nachrichten》2016,289(11-12):1341-1369
A critical radius function ρ assigns to each a positive number in a way that its variation at different points is somehow controlled by a power of the distance between them. This kind of function appears naturally in the harmonic analysis related to a Schrödinger operator with V a non‐negative potential satisfying some specific reverse Hölder condition. For a family of singular integrals associated with such critical radius function, we prove boundedness results in the extreme case . On one side we obtain weighted weak (1, 1) results for a class of weights larger than Muckenhoupt class A1. On the other side, for the same weights, we prove continuity from appropriate weighted Hardy spaces into weighted L1. To achieve the latter result we define weighted Hardy spaces by means of a ρ‐localized maximal heat operator. We obtain a suitable atomic decomposition and a characterization via ρ‐localized Riesz Transforms for these spaces. For the case of ρ derived from a Schrödinger operator, we obtain new estimates for many of the operators appearing in 27 . 相似文献