Carleson measures are ubiquitous in Harmonic Analysis. In the paper of
Fefferman--Kenig--Pipher in 1991 an interesting class of Carleson measures was
introduced for the need of regularity problems of elliptic PDE. These Carleson
measures were associated with $A_\infty$ weights. In discrete setting (we need
exactly discrete setting here) they were studied by Buckley's, where they were
associated with dyadic $A\infty^d$. Our goal here is to show that such
Carleson--Buckley measures (in discrete setting) exists for virtually any
positive function (weight).
We prove a multiparameter version of a classical theorem of Jones and Journe
on weak-star convergence in the Hardy space $H^1$.
We prove a multiparameter version of a classical theorem of Jones and Journe
on weak-star convergence in the Hardy space $H^1$.