BMO Functions and Carleson Measures with Values in Uniformly Convex Spaces
2010 ◽
Vol 62
(4)
◽
pp. 827-844
◽
Keyword(s):
AbstractThis paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let dA and dm denote Lebesgue measures on the unit disc D and the unit circle 𝕋, respectively. For 1 < q < ∞ and a Banach space B, we prove that there exists a positive constant c such thatholds for all trigonometric polynomials f with coefficients in B if and only if B admits an equivalent norm which is q-uniformly convex, whereThe validity of the converse inequality is equivalent to the existence of an equivalent q-uniformly smooth norm.
2006 ◽
Vol 2006
◽
pp. 1-11
Keyword(s):
2014 ◽
Vol 12
(03)
◽
pp. 1450024
Keyword(s):
1993 ◽
Vol 114
(1)
◽
pp. 25-30
◽
Keyword(s):
2003 ◽
Vol 67
(3)
◽
pp. 429-443
2014 ◽
Vol 35
(4)
◽
pp. 1009-1027
◽