LpL^p estimates for the Hilbert transforms along a one-variable vector field

Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, $L^2$ whenever $v$ is Lipschitz. We establish a wide range of $L^p$ estimates for this operator when $v$ is a measurable, non-vanishing, one-variable vector field in \bbr ^2. Aside from an $L^2$ estimate following from a simple trick with Carleson's theorem, these estimates were unknown previously. This paper is closely related to a recent paper of the first author (\cite{B2}).Comment: 25 page

Supply Side Structural Change

Growing economies often exhibit constant growth rates, constant interest rates, and an increasing urban share of their population. We show that the equilibrium path triggered by a capital-biased technological revolution can account for these regularities. This type of technological change can generate an aggregate production function that displays linear segments. As the economy moves along those segments, the interest rate and the growth rate are constant, and labor is gradually reallocated from the old (rural) techniques to the new (urban) techniques. The model predicts that developed countries must experience a sudden slowdown in their growth rates once their structural change is completed. Productivity, as measured by the Solow residuals, also displays a growth slowdown. Cross-country evidence supports these predictions of the model.

On the Collapse of Tubes Carried by 3D Incompressible Flows

We povide a test for numerical simulations for the collapse of regular tubes carried by a 3D incompressible flow. In particular, we obtain necessary conditions for 3D Euler to have a vortex tube collapse in finite time.Comment: 10 pages; the only change in this replacement is correction of " From" typos due to corruption in e-mai

Supply Side Structural Change

The interest rate and the rate of economic growth are often regarded as roughly constant as economies grow. Moreover, the agricultural sector and rural population typically shrink. We show that an otherwise standard growth model that includes a backward and an advanced sector can account for these regularities. The mechanism works as follows: as the economy accumulates capital, labor flows from the backward sector to the advanced one. This migration prevents the usual diminishing marginal returns of capital. As a result, the interest rate and the growth rate of the economy remain constant during the transition to the steady state. The model predicts that developed countries must experience a sudden slowdown in their growth rates once the backward sector fully disappears. Productivity, as measured by the Solow residuals, also must slow down. Cross-country evidence supports these predictions of the modelGrowth, Structural Change, Urbanization, Choice of Techniques, Productivity Slowdown