63 research outputs found
An equivalent condition to the Jensen inequality for the generalized Sugeno integral.
For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given
A weak notion of strict pseudo-convexity. Applications and examples
Let be a bounded -smoothly bounded domain
in For such a domain we define a new notion between strict
pseudo-convexity and pseudo-convexity: the size of the set of weakly
pseudo-convex points on is small with respect to Minkowski
dimension: near each point in the boundary there is at
least one complex tangent direction in which the slices of has a upper
Minkowski dimension strictly smaller than We propose to call this notion
"strong pseudo-convexity"; this word is free since "strict pseudo-convexity"
gets the precedence in the case where all the points in are
stricly pseudo-convex.
For such domains we prove that if is a separated sequence of points
contained in the support of a divisor in the Blaschke class, then a canonical
measure associated to is bounded. If moreover the domain is -regular,
and the sequence is dual bounded in the Hardy space then
the previous measure is Carleson.
As an application we prove a theorem on interpolating sequences in bounded
convex domains of finte type in
Examples of such pseudo-convex domains are finite type domains in
finite type convex domains in finite
type domains which have locally diagonalizable Levi form, domains with real
analytic boundary and of course, stricly pseudo-convex domains in
Domains like which are not of
finite type are nevertheless strongly pseudo-convex, in this sense.Comment: This is completely rewritten and expanded thanks to incisive
questions and a lot of deep suggestions done by the referee. This will appear
in Annali della Scuola Normale Superiore di Pis
Notes in Pure Mathematics & Mathematical Structures in Physics
These Notes deal with various areas of mathematics, and seek reciprocal
combinations, explore mutual relations, ranging from abstract objects to
problems in physics.Comment: Small improvements and addition
Recent Developments of Function Spaces and Their Applications I
This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation
Advances in Optimization and Nonlinear Analysis
The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics
LECTURES ON NONLINEAR DISPERSIVE EQUATIONS I
CONTENTS
J. Bona
Derivation and some fundamental properties of nonlinear dispersive waves equations
F. Planchon
Schr\"odinger equations with variable coecients
P. Rapha\"el
On the blow up phenomenon for the L^2 critical non linear Schrodinger Equatio
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