Let (X, d, μ) be a metric measure space satisfying Q-doubling condition (Q > 1) and an L2-Poincaré inequality. $${\cal L} = {\cal + V$$ Schrödinger operator on X, where L}$$ is non-negative generalized by Dirichlet form, V Muckenhoupt weight that satisfies reverse Hölder RHq for some q ⩾ 1)/2. We show solution to $$({\cal - \partial _t^2)u 0$$ X × ℝ+ the Carleson $$\mathop {{\rm{sub}}}\limits_{...

We prove L p $L^{p}$ -boundedness of variational Carleson operators for functions valued in intermediate UMD spaces. This provides quantitative information on the rate convergence partial Fourier integrals vector-valued functions. Our proof relies bounds wave packet embeddings into outer Lebesgue spaces time-frequency-scale space R + 3 $\mathbb {R}^{3}_{+}$ , which are focus this paper.

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.

We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.

Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.

We analyze reflection positive representations in terms of Hankel operators. This is motivated by the fact that operators are described their Carleson measures, whereas compatibility condition between and Hilbert spaces quite intricate. leads us to concept a representation triples (G,S,τ), where G group, τ an involutive automorphism S⊆G subsemigroup with τ(S)=S−1. For (Z,N,−idZ), corresponding ...