IJPAM: Volume 49, No. 1 (2008)

CONCLUDING REMARKS TO PAPER
PROPERTIES OF FUNCTION SPACES GENERATED
BY THE AVERAGED MODULI OF SMOOTHNESS
$International\ Journal\ of\ Pure\ and\ Applied\ Mathematics$,
Volume 41, No. 9 (2007)

Lubomir T. Dechevsky
R&D Group for Mathematical Modelling
Numerical Simulation and Computer Visualization
Institute for Information, Energy and Space Technology
Narvik University College
2, Lodve Lange's St., P.O. Box 385, Narvik, N-8505, NORWAY
e-mail: ltd@hin.no
url: https://ansatte.hin.no/ltd/


Abstract.This paper contains the material of Section 6 of [#!ltd-averaged!#] which has not been included in the original publication [#!ltd-averaged!#], due to an editorial error during the pre-print preparation of the journal issue containing the original submission (see the Editorial Note at the end of the presend text). The present paper consists of two sections: Section 1 provides the necessary preliminary orientation, while Section 2 coincides exactly with the unpublished Section 6 in the original submission. In the present paper, the list of references contains six publications (more precisely, [#!hgfei+!#,#!krugljak+!#,#!marchaud+!#,#!ltd+!#,#!ltd++!#,#!ltd+++!#]) which appeared only in Section 6 of the original submission, and have consequently not been included in the list of references in [#!ltd-averaged!#]. The present paper is an integral part of [#!ltd-averaged!#], and the two papers should be considered only together, as a single complete entity. The readers can also find the whole original material (as it was intended to appear in [#!ltd-averaged!#]) in the R$\&$D Report [#!ltd-averaged-rep!#].

Received: December 1, 2008

AMS Subject Classification: 41A17, 41A25, 41A65, 46B70, 46E30, 46E35, 47A30, 65J05, 26A33, 41A10, 41A29, 42B35, 46B42, 46E99, 46M35, 47H07, 47H19, 47H99, 65M10, 65N10, 65N15

Key Words and Phrases: convergence, approximation, error, regularity, positivity, monotonous, monotone, monotonicity, order preservation, constraint, bound, estimate, measure, boundedness, measurability, step, continuity, smoothness, integral modulus, local modulus, averaged modulus, Lebesgue space, Lorentz space, Jordan variation, Wiener-Young variation, Riemann-integrability, absolute continuity, Sobolev space, Besov space, Triebel-Lizorkin space, real interpolation space, complex interpolation space, sum of spaces, intersection of spaces, norm, seminorm, quasinorm, metric, metrizability, dual, duality, Banach space, Banach lattice, quasi-Banach space, quasi-Banach lattice, complete quasi-seminormed abelian group, Wiener amalgam space, embedding, isomorphism, isometry, inequality, linear operator, sublinear operator, $K$-functional, quasilinearizable

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 1