Displaying similar documents to “Systems of dyadic cubes in a doubling metric space”

Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes

Tuomas P. Hytönen (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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The vector-valued T(1) theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows one to circumvent the most subtle parts of the original arguments.

Improved Muckenhoupt-Wheeden inequality and weighted inequalities for potential operators.

Y. Rakotondratsimba (1995)

Publicacions Matemàtiques

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By a variant of the standard good λ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.

A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.

Xavier Tolsa (2001)

Publicacions Matemàtiques

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Given a doubling measure μ on R, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition...

Norm inequalities for potential-type operators.

Sagun Chanillo, Jan-Olov Strömberg, Richard L. Wheeden (1987)

Revista Matemática Iberoamericana

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The purpose of this paper is to derive norm inequalities for potentials of the form Tf(x) = ∫(Rn) f(y)K(x,y)dy,     x ∈ Rn, when K is a Kernel which satisfies estimates like those that hold for the Green function associated with the degenerate elliptic equations studied in [3] and [4].

Weak type estimates for operators of potential type

Richard Wheeden, Shiying Zhao (1996)

Studia Mathematica

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We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.