Nonlinear potential theory on the ball, with applications to exceptional and boundary interpolation sets.

Fractional derivatives of pointwise multipliers between holomorphic spaces

“…When 0 < s < n/p, these measures can be characterized in terms of non-isotropic Riesz capacities (see [1] and [17]). …”

On Weighted Toeplitz, Big Hankel Operators and Carleson Measures

“…In [2,13,14], it is proved that if (n−1)/p < s ≤ n/p, i.e. if 0 ≤ n−sp < 1, then µ ∈ CM p s if and only if µ satisfies condition (2.5).…”

“…We will denote by CM p s the set of these measures, and by µ CM p s the norm of the embedding B p s ⊂ L p (µ). The Carleson measures for Besov and Hardy-Sobolev spaces have been studied by many authors ( [2,[4][5][6]11,13,14,16,22,25] among others). See Sect.…”

Carleson measures for weighted Hardy-sobolev spaces

“…But for n − sp ≥ 0, and n > 1, the characterization of the Carleson measures for H p s still remains open. In the case where we are "near" the regular case, that is when n − sp < 1 it is shown in [AhCo], [CohVe1] and [CohVe2], that the Carleson measures for H One of the main purposes of this paper is to extend this situation to H p s (w) for w a weight in A p . If E ⊂ S n is measurable, we define CARLESON MEASURES FOR H p s (w)…”