No abstract

Part 3. Analytic theory 11. Statements and reduction to the free case 12. The multiple mapping Γ 13. The space L 1 δ 14. The almost orthogonal decomposition 15. The kernel of (T j T * j ) N ; the L 2 theorem 16. The L p argument; preliminaries 17. Further L 2 estimates 18. The L p estimates; conclusion 19. The maximal function 20. The smoothing property 21. Complements and remarks Part 4. Appendix 22. Proof of the lifting theorem References

Let 10jI be a lacunary sequence going to zero.Let y(t) = (ti, . . , tI,). Define M*fx) = sup I f(x + tY(0j))dtl.We prove IIM*flIj S A, llflIp, 1 < p < ao.

No abstract

We study a class of operators on nilpotent Lie groups G given by convolution with flag kernels. These are special kinds of product-type distributions whose singularities are supported on an increasing subspace (0)We show that product kernels can be written as finite sums of flag kernels, that flag kernels can be characterized in terms of their Fourier transforms, and that flag kernels have good regularity, restriction, and composition properties.We then apply this theory to the study of the g b -complex on certain quadratic CR submanifolds of C n . We obtain L p regularity for certain derivatives of the relative fundamental solution of g b and for the corresponding Szego projections onto the null space of g b by showing that the distribution kernels of these operators are finite sums of flag kernels.