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We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.

Products of quasi-continuous functions

Tomasz Natkaniec (1990)

Mathematica Slovaca

Products of simply continuous and quasicontinuous functions

Ján Borsík (1995)

Mathematica Slovaca

Professor Rudolf Gorenflo and his Contribution to Fractional Calculus

Luchko, Yury, Mainardi, Francesco, Rogosin, Sergei (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversaryThis paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo - a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fractional Calculus and its applications...

Progress of iteration theory since 1981.

György Targonski (1995)

Aequationes mathematicae

Properties of connected functions in terms of their levels

K. Garg (1977)

Fundamenta Mathematicae

Properties of functions of generalized bounded variation

R. G. Vyas (2006)

Matematički Vesnik

Pseudo almost periodicity of fractional integro-differential equations with impulsive effects in Banach spaces

Zhinan Xia (2017)

Czechoslovak Mathematical Journal

In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic $P C$ -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic $P C$ -mild solution of a two-dimensional impulsive fractional...

Pseudo-symmetric differentiation

H. W. Pu, H. H. Pu (1989)

Colloquium Mathematicae

Quadratic integral equations in reflexive Banach space

Hussein A.H. Salem (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

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Prevalence of backward stochastic differential equations with unique solution.

Prevalence of some known typical properties.

Přímý důkaz průkladného vzorce Lagrange-ova

Problèmes d'optimisation dépendant d'un paramètre à valeurs dans un espace de Banach

Problèmes variationnels et théorie du potentiel non linéaire

Processus gaussiens à variation finie

Product rule and chain rule estimates for the Hajłasz gradient on doubling metric measure spaces