The extremely asymmetric radio structure of the z=3.1 radio galaxy B3 J2330+3927

We report on 1.7 and 5.0 GHz observations of the z=3.087 radio galaxy B3 J2330+3927, using the Very Long Baseline Array (VLBA), and archival 1.4 and 8.4 GHz Very Large Array (VLA) data. Our VLBA data identify a compact, flat spectrum (\alpha_{1.7 GHz}^{5 GHz} = -0.2 +/- 0.1; S_\nu ~ \nu^\alpha) radio component as the core. The VLA images show that the fraction of core emission is very large (f_c \approx 0.5 at 8.4 GHz), and reveal a previously undetected, very faint counterjet, implying a radio lobe flux density ratio R >= 11 and a radio lobe distance ratio Q \approx 1.9. Those values are much more common in quasars than in radio galaxies, but the optical/near-IR spectra show a clear type II AGN for B3 J2330+3927, confirming that it is indeed a radio galaxy. Unlike all other radio galaxies, the bright Ly-\alpha emitting gas is located towards the furthest radio arm. We argue against environmental and relativistic beaming effects being the cause of the observed asymmetry, and suggest this source has intrinsically asymmetric radio jets. If this is the case, B3 J2330+3927 is the first example of such a source at high redshift, and seems to be difficult to reconcile with the unified model, which explains the differences between quasars and radio galaxies as being due to orientation effects.Comment: 6 pages, 3 figures, to appear as a Letter to MNRA

End-point estimates for iterated commutators of multilinear singular integrals

Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted results involving the vectors weights of the multilinear Calderon-Zygmund theory recently introduced in the literature. Some better than expected estimates for certain multilinear operators are presented too.Comment: A typo in the original manuscript lead to overlook a gap in one of our arguments which has been fixed. The new arguments are provided in the proof of Theorem 3.1 in Section 3. With the exception of some new notation introduced and some minor changes in wording in a few places, those new details are the only modifications to the original manuscrip

The multilinear strong maximal function

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Certain bilinear interpolation results between distributional estimates, such as that obtained for the multivariable strong maximal function, are also proved.Comment: appeared in J. of Geometric Ana

Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the unstable solitary waves which belong to the frontier between expanding and collapsing solutions and to provide an oscillating solitonic structure, some sort of breather-type solution. We obtain precise conditions on the control parameters to achieve the stabilization and compare our results with accurate numerical simulations of the nonlinear Schrodinger equation. Because of the application of these ideas to matter waves these solutions are some sort of matter breathers