The Q_pcorona theorem

Multipliers of Möbius invariant Q s spaces

“…That (i) implies (ii) it is proved in Theorem 1.3 of [14]. So, assume that f ∈ H (D) satisfies (ii), and let g ∈ Q s .…”

“…So, it seems that condition (3) will play a crucial role in order to characterize the pointwise multipliers of Q s . Xiao [14] proves that, when 0 < s < 1, the condition (3) is necessary for a function g to be in M(Q s ), and moreover he conjectures that this condition is also sufficient.…”

Boundary multipliers of a family of Möbius invariant function spaces

“…It is worth mentioning that Stegenga [24] characterized the multipliers of bounded mean oscillation spaces on the unit circle (see also [17]), and Brown and Shields [5] described the pointwise multipliers of the Bloch space. A characterization of the pointwise multipliers M(Q s (D)) was obtained in [18] proving a conjecture stated in [28]. See [10,17,22,25,27,35] for more results on pointwise multipliers of function spaces.…”

“…Note that, when p 1 = p 2 = 2 and s = r, part (1) of Theorem 1.1 proves Conjecture 2.5 stated in [28]. However, as seen in the proof, this conjecture is an immediate consequence of the results and methods in [18].…”

The essential spectrum of holomorphic Toeplitz operators on Hpspaces

“…[3]. The equality σ r (T g , X) = g(D) has been proved for a large number of other function spaces X in strictly pseudoconvex domains such as various Besov spaces ( [7] and [8]) and Q p spaces ( [13] and [4]). In each case, the g j are assumed to be multipliers on the space X in question.…”