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Two-weight weak type maximal inequalities in Orlicz classes

Luboš Pick (1991)

Studia Mathematica

Necessary and sufficient conditions are shown in order that the inequalities of the form ϱ ( M μ f > λ ) Φ ( λ ) C ʃ X Ψ ( C | f ( x ) | ) σ ( x ) d μ , or ϱ ( M μ f > λ ) C ʃ X Φ ( C λ - 1 | f ( x ) | ) σ ( x ) d μ hold with some positive C independent of λ > 0 and a μ-measurable function f, where (X,μ) is a space with a complete doubling measure μ, M μ is the maximal operator with respect to μ, Φ, Ψ are arbitrary Young functions, and ϱ, σ are weights, not necessarily doubling.

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

Gladis Pradolini, Jorgelina Recchi (2018)

Czechoslovak Mathematical Journal

Let μ be a nonnegative Borel measure on d satisfying that μ ( Q ) l ( Q ) n for every cube Q 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...

Uniform bounds for the bilinear Hilbert transforms (II).

Xiaochun Li (2006)

Revista Matemática Iberoamericana

We continue the investigation initiated in [Grafakos, L. and Li, X.: Uniform bounds for the bilinear Hilbert transforms (I). Ann. of Math. (2)159 (2004), 889-933] of uniform Lp bounds for the family of bilinear Hilbert transformsHα,β(f,g)(x) = p.v. ∫R f(x - αt) g (x - βt) dt/t.

Unique continuation for the solutions of the laplacian plus a drift

Alberto Ruiz, Luis Vega (1991)

Annales de l'institut Fourier

We prove unique continuation for solutions of the inequality | Δ u ( x ) | V ( x ) | u ( x ) | , x Ω a connected set contained in R n and V is in the Morrey spaces F α , p , with p ( n - 2 ) / 2 ( 1 - α ) and α &lt; 1 . These spaces include L q for q ( 3 n - 2 ) / 2 (see [H], [BKRS]). If p = ( n - 2 ) / 2 ( 1 - α ) , the extra assumption of V being small enough is needed.

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G. Kyriazis (1998)

Studia Mathematica

We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces C p α ( d ) , 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the C p α ( d ) spaces in terms of the coefficients of wavelet decompositions.

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