Two-weight norm inequalities for fractional maximal operators on spaces of generalized homogeneous type

In this paper a characterization is given for a pairs of weights (w,v) for which the fractional maximal operator is bounded from when is a space of generalized homogeneous type introduced by A. Carbery et al. [4].     

齐型空间上的Orlicz Morrey空间极大算子有界性

In this paper, the characterization of boundedness of Hardy-Littlewood maximal operators in Orlicz-Morrey spaces L^Фψ（X,μ） of homogeneous type is founded.     

Weighted norm inequalities for the maximal singular integral operators on spaces of homogeneous type

Weighted norm inequalities with general weights are established for the maximal singular integral operators on spaces of homogeneous type, when the kernel satisfies a Hörmander regularity condition on one variable and a Hölder regularity condition on the other variable.     

Composition of fractional Orlicz maximal operators and A 1-weights on spaces of homogeneous type

For a Young function θ with 0 ≤α 〈 1, let Mα,θ be the fractional Orlicz maximal operator defined in the context of the spaces of homogeneous type （X, d, μ） by Mα,θf（x） = supx∈（B）α ｜｜f｜｜θ,B, where ｜｜f｜｜θ,B is the mean Luxemburg norm of f on a ball B. When α= 0 we simply denote it by Me. In this paper we prove that if Ф and ψare two Young functions, there exists a third Young function θ such that the composition Mα,ψ o MФ is pointwise equivalent to Mα,θ. As a consequence we prove that for some Young functions θ, if Mα,θf 〈∞a.e. and δ ∈（0,1） then （Mα,θf）δ is an A1-weight.     

Maximal operators on spaces of homogeneous type

We avoid the assumption given in the work of C. Pérez and R. Wheeden (2001) to prove boundedness properties of certain maximal functions in a general setting of the spaces of homogeneous type with infinite measure. In addition, an example shows that the result can be false if the space has finite measure.

     

Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces

Let μ be a nonnegative Borel measure on R ^d satisfying that μ(Q) ? l(Q)ⁿ for every cube Q ? R ⁿ , where l(Q) is the side length of the cube Q and 0 < n ? d.We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function B in the context of non-homogeneous spaces related to the measure μ. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W.Wang, C. Tan, Z. Lou (2012).     

A maximal function characterization of Hardy spaces on spaces of homogeneous type

A new maximal funtion is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces. This work is supported by NSF.     

Weighted reverse weak type inequality for general maximal functions

Necessary and sufficient conditions are found to be imposed on a pair of weights, for which a weak type two-weighted reverse inequality holds, in the case of general maximal functions defined in homogenous type spaces.     

Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type

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 L^p(v) to L^q,∞(u), 1<p?q<∞, provided the pair of weights (u,v) verifies a Muckenhoupt condition with a “power-bump” on the weight u.     

Weak type estimates for some maximal operators on Hardy spaces

We show that the lacunary maximal operator associated to a compact smooth hypersurface on which the Gaussian curvature nowhere vanishes to infinite order maps the standard Hardy space H ¹ to L ^1,∞ . (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundedness of para-product operators on spaces of homogeneous type

We obtain the boundedness of Calderón-Zygmund singular integral operators T of non-convolution type on Hardy spaces H ^p (X) for 1/(1 + ε) < p ? 1, where X is a space of homogeneous type in the sense of Coifman and Weiss (1971), and ε is the regularity exponent of the kernel of the singular integral operator T. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.     

Harnack's inequality on homogeneous spaces

We consider a homogeneous space X=(X, d, m) of dimension v≥1 and a local regular Dirichlet form in L² (X, m). We prove that if a Poincaré inequality holds on every pseudo-ball B(x, R) of X, then an Harnack's inequality can be proved on the same ball with local characteristic constant c₀ and c₁ Entrata in Redazione il 19 giugno 1996.     

Weighted norm inequalities for the maximal function on spaces of homogeneous type

A characterization is obtained for weight function v for which the Hardy-Littlewood operator relative to a metric d is bounded from L^P(X, wdμ) to L^P(X, vdμ) for some nontrivial w, where (X, d, μ) is a space of homogeneous type. Supported by Natural Science Foundation of China.     

Weak type estimates for some maximal operators on the weighted Hardy spaces

Weighted weak type estimates are proved for some maximal operators on the weighted Hardy spacesH _ω ^p (0 <p < 1, ω ∈A ₁) (0<p<1, ω∞A₁); in particular, weighted weak type endpoint estimates are obtained for the maximal operators arising from the Bochner-Riesz means and the spherical means onH _ω ^p .     

Weighted estimates for commutators of potential operators on spaces of homogeneous type

We derive some strong type and weak type weighted norm estimates which relate the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.     

Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications

In this paper, using the discrete Calderon reproducing formula on spaces of homogeneous type obtained by the author, we obtain the Plancherel-Pôlya type inequalities on spaces of homogeneous type. These inequalities give new characterizations of the Besov spaces and the Triebel-Lizorkin spaces on spaces of homogeneous type introduced earlier by the author and E. T. Sawyer and also allow us to generalize these spaces to the case where . Moreover, using these inequalities, we can easily show that the Littlewood-Paley -function and -function are equivalent on spaces of homogeneous type, which gives a new characterization of the Hardy spaces on spaces of homogeneous type introduced by Macias and Segovia.