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On the Continuity of the Nemytskij Operator between the Spaces ๐ฟ๐1(๐) and ๐ฟ๐2(๐)
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Marek Galewski
Verรถffentlicht/Copyright:
10. Mรคrz 2010
Abstract
We provide a generalized sufficient condition for the continuity of the Nemytskij operator between ๐ฟ๐1(๐) and ๐ฟ๐2(๐). An example is given.
Key words and phrases:: Nemytskij operator; continuity; ๐ฟ๐(๐)-space; generalized growth conditions
Received: 2004-12-08
Revised: 2005-07-20
Revised: 2006-02-16
Published Online: 2010-03-10
Published in Print: 2006-June
ยฉ Heldermann Verlag
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Artikel in diesem Heft
- Semimartingale Local Time and the American Put Option
- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces ๐ฟ๐1(๐) and ๐ฟ๐2(๐)
- Monadic ๐ต๐ฟ-Algebras
- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (๐, ๐)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to โOn a Singular Direction of a Meromorphic Functionโ
Schlagwรถrter fรผr diesen Artikel
Nemytskij operator;
continuity;
๐ฟ๐(๐)-space;
generalized growth conditions
Artikel in diesem Heft
- Semimartingale Local Time and the American Put Option
- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces ๐ฟ๐1(๐) and ๐ฟ๐2(๐)
- Monadic ๐ต๐ฟ-Algebras
- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (๐, ๐)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to โOn a Singular Direction of a Meromorphic Functionโ