A1-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions

A characterization of the weighted weak type Coifman–Fefferman and Fefferman–Stein inequalities

“…The following lemma is the above mentioned weaker version of the result in [15]. where q = q(n) < 1.…”

“…As we have mentioned in the Introduction, Theorem 1.1 can be deduced by combining the ingredients from Sections 3 and 4 with the result of D. Rutsky [15]. We give a simplified proof of a weaker version of this result, which is enough for our purposes.…”

“…A non-trivial part of Theorem 1.1 is the implication (ii) ⇒ (i). Here we essentially use a recent interesting result of D. Rutsky [15] saying that for a BFS X, the boundedness of every Riesz transform R j on X is equivalent to the boundedness of M on X and X ′ , where X ′ is the space associate to X.…”

“…n, are bounded on MX. It remains to apply the above-mentioned result of D. Rutsky [15] to MX instead of X.…”

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

“…Next, we obtain a pointwise estimate for the composition of M with the maximal Calderón-Zygmund operator, which along with (ii) and the boundedness of M on MX implies that R j , and so R j , j=1, ...n, are bounded on MX. It remains to apply the above-mentioned result of D. Rutsky [15] to MX instead of X.…”