Sublinear operators with rough kernel generated by Calderón–Zygmund operators and their commutators on generalized Morrey spaces

Adams-Spanne type estimates for parabolic sublinear operators and their commutators with rough kernels on parabolic generalized Morrey spaces

“…Proof. Let 1 < p < ∞ and s ′ ≤ p. The estimation of the norm of the operator, that is, the boundedness in the vanishing generalized Morrey space follows from Lemma 2.1. in [5] and condition (3.2)…”

“…So it is sufficient to prove that (3.5) lim To show that sup x∈R n ϕ 2 (x, r) −1 T Ω f Lp(B(x,r)) < ǫ for small r, we split the right hand side of (2.1) in Lemma 2.1. in [5]:…”

“…Thus we only have to prove that ϕ2(x,r) < ǫ for small r, we split the right-hand side of (2.1) in Lemma 3 in [6]:…”

“…The proof follows more or less the same lines as for Theorem 1, but now the arguments are different due to the necessity to introduce the logarithmic factor into the assumptions. Let s ′ ≤ p. The estimation of the norm of the operator, that is, the boundedness in the vanishing generalized Morrey space follows from Lemma 2.2. in [5] and condition (3.13)…”

On the behavior of a class of fractional type rough higher order commutators on generalized weighted Morrey spaces

“…all balls B (see [1] for more details). Now, let us consider the Muckenhoupt-Wheeden class A (p, q) in [5].…”