Результаты исследований: Научные публикации в периодических изданиях › статья
Weak integral conditions for BMO. / Logunov, A.A.; Slavin, L.; Stolyarov, D.M.; Vasyunin, V.; Zatitskiy, P.B.
в: Proceedings of the American Mathematical Society, Том 143, № 7, 2015, стр. 2913-2926.Результаты исследований: Научные публикации в периодических изданиях › статья
}
TY - JOUR
T1 - Weak integral conditions for BMO
AU - Logunov, A.A.
AU - Slavin, L.
AU - Stolyarov, D.M.
AU - Vasyunin, V.
AU - Zatitskiy, P.B.
PY - 2015
Y1 - 2015
N2 - © 2015 American Mathematical Society We study the question of how much one can weaken the defining condition of BMO. Specifically, we show that if Q is a cube in Rn and h: [0,∞) → [0,∞) is such that h(t)→∞ as t→∞, then sup J subcube Q 1 |J|_ J h ϕ – 1 |J| J ϕ _<∞ =⇒ ϕ ∈ BMO(Q). Under some additional assumptions on h we obtain estimates on _ϕ_BMO in terms of the supremum above. We also show that even though the limit condition on h is not necessary for this implication to hold, it becomes necessary if one considers the dyadic BMO.
AB - © 2015 American Mathematical Society We study the question of how much one can weaken the defining condition of BMO. Specifically, we show that if Q is a cube in Rn and h: [0,∞) → [0,∞) is such that h(t)→∞ as t→∞, then sup J subcube Q 1 |J|_ J h ϕ – 1 |J| J ϕ _<∞ =⇒ ϕ ∈ BMO(Q). Under some additional assumptions on h we obtain estimates on _ϕ_BMO in terms of the supremum above. We also show that even though the limit condition on h is not necessary for this implication to hold, it becomes necessary if one considers the dyadic BMO.
M3 - Article
VL - 143
SP - 2913
EP - 2926
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 7
ER -
ID: 3977178