Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 949-955

A₁ WEIGHTS ON R, AN ALTERNATIVE APPROACH

Eleftherios N. Nikolidakis

National and Kapodistrian University of Athens, Department of Mathematics
GR-157 84, Athens, Greece; lefteris 'at' math.uoc.gr

Abstract. We will prove that if Φ belongs to the class A₁(R) with constant c ≥ 1 then the decreasing rearrangement of Φ, belongs to the same class with constant not more than c. We also find for such Φ the exact best possible range of those p > 1 for which Φ ∈ L^p, for any such Φ. In this way we provide alternative proofs of the results that appear in a previous work of Bojarski, Sbordone and Wik.

2010 Mathematics Subject Classification: Primary 42B25.

Key words: A₁-Muckenhoupt weights, decreasing rearrangement.

Reference to this article: E.N. Nikolidakis: A₁ weights on R, an alternative approach. Ann. Acad. Sci. Fenn. Math. 40 (2015), 949-955.

Full document as PDF file

doi:10.5186/aasfm.2015.4053

A1 WEIGHTS ON R, AN ALTERNATIVE APPROACH

Eleftherios N. Nikolidakis

A₁ WEIGHTS ON R, AN ALTERNATIVE APPROACH