We study BMO spaces associated with semigroup of operators on noncommutative function spaces (i.e. von Neumann algebras) and apply the results to boundedness of Fourier multipliers on non-abelian discrete groups. We prove an interpolation theorem for BMO spaces and prove the boundedness of a class of Fourier multipliers on noncommutative Lp spaces for all 1 < p < ∞, with optimal constants in p....

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: v(x)xρ is equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). Let A be the averaging operator given by (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞). First, we prove that the operator A : L((0,+∞); v)→ L((0,+∞); v) is bounded if and only if the operator A : L((0,+∞); v)→ L((0,+∞);w) i...

In this note the authors prove the Lp(Rn×Rm)-boundedness for a class of maximal singular integral operators with rough kernel on product spaces. This extends a result obtained by Chen and Wang in 1992.

In this article, we prove the boundedness and compactness of localization operators associated with Stockwell transforms, which depend on a symbol and two windows, on Lp(R), 1 ≤ p ≤ ∞.

In this paper, we investigate the boundedness of a square function operator from ergodic theory acting on noncommutative Lp-spaces. The main result is weak type (1,1) estimate operator. We also show (L∞,BMO) estimate, and thus all strong (Lp,Lp) estimates by interpolation. new difficulty lies in fact that kernel does not enjoy any regularity, while Lipschitz regularity assumption crucial showin...