Littlewood-Paley -Functions and Multipliers for the Laguerre Hypergroup

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

On Bilinear Littlewood-paley Square Functions

On the real line, let the Fourier transform of kn be k̂n(ξ) = k̂(ξ−n) where k̂(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x + y)g(x − y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove that ∞ ∑ n=−∞ ‖Sn(f, g)‖2 ≤ C‖f‖p‖g‖q . The constant C depends only upon k.

Rubio de Francia’s Littlewood-Paley inequality for operator-valued functions

We prove Rubio de Francia’s Littlewood-Paley inequality for arbitrary disjoint intervals in the noncommutative setting, i.e. for functions with values in noncommutative L-spaces. As applications, we get sufficient conditions in terms of q-variation for the boundedness of Schur multipliers on Schatten classes.

On the littlewood-paley and lusin functions in higher dimensions.

Remarks on Square Functions in the Littlewood-paley Theory

We prove that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on L p w , 1 < p < ∞, w ∈ Ap (the weights of Muckenhoupt). Then, we give some applications to the Carleson measures on the upper half space.