From Weak-type Weighted Inequality to Pointwise Estimate for the Decreasing Rearrangement

AGORA, ELONA; ANTEZANA, JORGE; BAENA-MIRET, SERGI; CARRO, MARÍA J.

THE JOURNAL OF GEOMETRIC ANALYSIS

SPRINGER

Año: 2021 vol. 32

1050-6926

We shall prove pointwise estimates for the decreasing rearrangement of Tf, where T covers a wide range of interesting operators in Harmonic Analysis such as operators satisfying a Fefferman–Stein inequality, the Bochner-Riesz operator, rough operators, sparse operators, Fourier multipliers. In particular, our main estimate is given in terms of the Hardy and adjoint of Hardy operator with some weight φ, which is determined by the Muckenhoupt Ap- weight norm behavior of the operator.