General types of spherical mean operators and $K$-functionals of fractional orders

Thaís Jordão; Xingping Sun

doi:10.3934/cpaa.2015.14.743

Article Contents

2015, Volume 14, Issue 3: 743-757. Doi: 10.3934/cpaa.2015.14.743

This issue Previous Article Next Article Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities

General types of spherical mean operators and $K$-functionals of fractional orders

Thaís Jordão^1, and
Xingping Sun^2,

1.
Departamento de Matemática, Universidade de São Paulo (ICMC - USP), São Carlos, SP 13560-970
2.
Department of Mathematics, Missouri State University, Springfield, MO 65804

Received: February 28, 2014

Revised: August 31, 2014

Published: April 2015

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Abstract

We design a general type of spherical mean operators and employ them to approximate $L_p$ class functions. We show that optimal orders of approximation are achieved via appropriately defined K-functionals of fractional orders.

Keywords:

Mathematics Subject Classification: Primary: 40A05, 41A36; Secondary: 41A60, 45C05, 47A75.

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