Morse-Sard theorem for delta-convex curves
Let be a delta-convex mapping, where is an open interval and a Banach space. Let be the set of critical points of . We prove that has zero -dimensional Hausdorff measure.
Morse-Sard theorem for real-analytic functions
Moser's Inequality for a class of integral operators
Let 1 < p < ∞, q = p/(p-1) and for define , x > 0. Moser’s Inequality states that there is a constant such that where is the unit ball of . Moreover, the value a = 1 is sharp. We observe that f where the integral operator has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for the analogue...
Moser-Trudinger and logarithmic HLS inequalities for systems
We prove several optimal Moser–Trudinger and logarithmic Hardy–Littlewood–Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere , on a bounded domain and on all of . In some cases we also address the question of existence of minimizers.
Mulitply Periodic Real Functions and Their Period Sets.
Multidimensional extension of L. C. Young's inequality.
Multidimensional Hilbert-type inequalities with a homogeneous kernel.
Multidimensional integral inequalities with homogeneous weights.
Multidimensional Opial inequalities for functions vanishing at an interior point
In this paper we generalize Opial inequalities in the multidimensional case over balls. The inequalities carry weights and are proved to be sharp. The functions under consideration vanish at the center of the ball.
Multifunctions of two variables: examples and counterexamples
A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.
Multifunctions with selections of convex and concave type.
Multiple integrals evaluated by functional equations
Multiple Lebesgue integration on time scales.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication of fuzzy quantities
Multiplication of subharmonic functions.
Multiplicative concavity of the integral of multiplicatively concave functions.
Multiplicative functionals on algebras of differentiable functions.
Let Ω be an open subset of a real Banach space E and, for 1 ≤ m ≤, let Cm(Ω) denote the algebra of all m-times continuously Fréchet differentiable real functions defined on Ω. We are concerned here with the question as to wether every nonzero algebra homomorphism φ: Cm(Ω) → R is given by evaluation at some point of Ω, i.e., if there exists some a ∈ Ω such that φ(f) = f(a) for each f ∈ Cm(Ω). This problem has been considered in [1,4,5] and [6]. In [6], a positive answer is given in the case that...
Multiplicity and uniqueness for a class of discrete fractional boundary value problems
The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).
Multipliers for generalized Riemann integrals in the real line
We use an elementary method to prove that each function is a multiplier for the -integral.