Weighted Harmonic Bloch Spaces on the Ball

Singular Integral Operators with Bergman–Besov Kernels on the Ball

“…Here's another similar result adapted from [5,Lemma 2.3]. where p k is a holomorphic homogeneous polynomial of degree k. Then by Definition 3.1 and (2) again,…”

“…The next lemma is adapted from[5, Lemma 3.2]. To see what it means, first check that K q (0, z) = 1 for all z ∈ B.…”

A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces

“…α and also can be extended to the whole range α ∈ R. The properties of this extended family are studied in detail in [5] and will be reviewed in Section 2.…”

“…Definition 2.3. For α ∈ R, we define the harmonic Bloch space b ∞ α to consist of all f ∈ h(B) for which I t s f belongs to L ∞ α for some s, t satisfying (see [5]) α + t > 0.…”

Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of

“…Our use of follows [16] and [7], which is more logical in view of the operators and conforms well with the notation of , so the usual Bloch space  ∞ 0 =  ∞ corresponds to = 0. Most other authors use + 1 while [29] uses − where we use .…”