A note on the Coifman–Fefferman and Fefferman–Stein inequalities

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore’s inequality for the moduli of smoothness and a logarithmic variant of Bennett–DeVore–Sharpley’s inequality for rearrangements. As a consequence, we improve the classical Stein–Zygmund embedding deriving B ˙ ∞ d / p L p , ∞ ( R d ) ↪ BMO ( R d ) \dot {B}^{d/p}_\infty L_{p,\infty }(\mathbb {R}^d) \hookrightarrow \text {BMO}(\mathbb {R}^d) for 1 > p > ∞ 1 > p > \infty . Moreover, these results are also applied to establish new Fefferman–Stein inequalities, Calderón–Scott type inequalities, and extrapolation estimates. Our approach is based on the limiting interpolation techniques.

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A note on the Coifman–Fefferman and Fefferman–Stein inequalities

Abstract: A condition on a Banach function space X is given under which the Coifman-Fefferman and Fefferman-Stein inequalities on X are equivalent.

Cited by 2 publications

References 10 publications

Pointwise estimates for rough operators with applications to Sobolev inequalities

Pointwise estimates for rough operators with applications to Sobolev inequalities

New estimates for the maximal functions and applications

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