5,860 research outputs found
Boundedness of Pseudodifferential Operators on Banach Function Spaces
We show that if the Hardy-Littlewood maximal operator is bounded on a
separable Banach function space and on its associate space
, then a pseudodifferential operator
is bounded on whenever the symbol belongs to the
H\"ormander class with ,
or to the the Miyachi class
with ,
. This result is applied to the case of
variable Lebesgue spaces .Comment: To appear in a special volume of Operator Theory: Advances and
Applications dedicated to Ant\'onio Ferreira dos Santo
Norm inequalities for the minimal and maximal operator, and differentiation of the integral
We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)
Norm inequalities for the minimal and maximal operator, and differentiation of the integral
We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)
Correction of Errors During The Manufacture by Computer Numerical Control (CNC) of Blades for an Axial Hydrokinetic Turbine
The design and manufacture of new systems for providing electric power to non-interconnected areas is one of the challenges for engineering. There are several alternatives, including water or wind-power generation systems, where hydrokinetic turbines are highlighted. This work establishes the methodology, identification and correction of errors generated during the manufacture by machining, using CAD/CAPP/CAM techniques, for an axial hydrokinetic turbine. During the manufacturing process, the generation of an error on the edges of the blades was identified, which was attributed to problems in the design of the model since the degrees of freedom of the manufacturing system used were not considered. For the manufacture of complex surfaces in the design of models, the most extreme points of the surfaces in contact must match the tangent edges to ensure that the tools of machining can reach them with the trajectories generated from the CAM
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Depth profile of the ferromagnetic order in a YBaCuO / LaCaMnO superlattice on a LSAT substrate: a polarized neutron reflectometry study
Using polarized neutron reflectometry (PNR) we have investigated a
YBa2Cu3O7(10nm)/La2/3Ca1/3MnO3(9nm)]10 (YBCO/LCMO) superlattice grown by pulsed
laser deposition on a La0.3Sr0.7Al0.65Ta0.35O3 (LSAT) substrate. Due to the
high structural quality of the superlattice and the substrate, the specular
reflectivity signal extends with a high signal-to-background ratio beyond the
fourth order superlattice Bragg peak. This allows us to obtain more detailed
and reliable information about the magnetic depth profile than in previous PNR
studies on similar superlattices that were partially impeded by problems
related to the low temperature structural transitions of the SrTiO3 substrates.
In agreement with the previous reports, our PNR data reveal a strong magnetic
proximity effect showing that the depth profile of the magnetic potential
differs significantly from the one of the nuclear potential that is given by
the YBCO and LCMO layer thickness. We present fits of the PNR data using
different simple block-like models for which either a ferromagnetic moment is
induced on the YBCO side of the interfaces or the ferromagnetic order is
suppressed on the LCMO side. We show that a good agreement with the PNR data
and with the average magnetization as obtained from dc magnetization data can
only be obtained with the latter model where a so-called depleted layer with a
strongly suppressed ferromagnetic moment develops on the LCMO side of the
interfaces. The models with an induced ferromagnetic moment on the YBCO side
fail to reproduce the details of the higher order superlattice Bragg peaks and
yield a wrong magnitude of the average magnetization. We also show that the PNR
data are still consistent with the small, ferromagnetic Cu moment of 0.25muB
that was previously identified with x-ray magnetic circular dichroism and x-ray
resonant magnetic reflectometry measurements on the same superlattice.Comment: 11 pages, 7 figure
Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms
Given any smooth toric surface S, we prove a SYM-HILB correspondence which
relates the 3-point, degree zero, extended Gromov-Witten invariants of the
n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal
Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As
we do not specialize the values of the quantum parameters involved, this result
proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture
for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of
reconstructing the cup product for Hilb^n(S) from the orbifold invariants of
[Sym^n(S)].Comment: Revised versio
Finite element approximation of the -Laplacian
We study a~priori estimates for the Dirichlet problem of the
-Laplacian,
We show that the gradients of the finite element approximation with zero
boundary data converges with rate if the exponent is
-H\"{o}lder continuous. The error of the gradients is measured in the
so-called quasi-norm, i.e. we measure the -error of
- …