A note on  weights: Pasting weights and changing variables.

In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces H (R x R ) and a description of their duals when p is close to 1.

Weighted norm inequalities for maximal functions from the Muckenhoupt conditions.

Y. Rakotondratsimba (1994)

Publicacions Matemàtiques

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For some pairs of weight functions u, v which satisfy the well-known Muckenhoupt conditions, we derive the boundedness of the maximal fractional operator M (0 ≤ s < n) from L to L with q < p.

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