[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2020.33.1.57

BOUNDEDNESS OF THE SPECTRA OF BASE FUNCTIONS FOR NEW SPACES

Pak, Hee Chul (Department of Mathematics Dankook University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.33, no.1, 2020 , pp. 57-63 More about this Journal

Abstract

We investigate the boundedness of the spectrum of a convex base function for a new function space. The result guarantees the continuity of the Calderón-Zygmund operators on the new space.

Keywords

spectrum of base function; new function space; singular integral; $Calder{\acute{o}}n$ -Zygmund operator;

Citations & Related Records

Reference

1	R. Adams, Sobolev spaces, 2nd Edition, Academic press, Amsterdam, 2003.
2	H-C. Pak, Existence of solutions for a nonlinear elliptic equation with general flux term, Fixed Point Theory and Appl., 2011 (2011), Article ID 496417.
3	H-C. Pak and S-H. Chang, A new function space $L_{\alpha}(X)$ - Version 1.1, J. Chungcheong Math. Soc., 21 (2008), 471-481.
4	H-C. Pak and S-H. Chang, Poincare's inequality on a new function space $L_{\alpha}(X)$ , J. Chungcheong Math. Soc., 22 (2009), 309-318.
5	H-C. Pak and Y-J. Park, Trace operator and a nonlinear boundary value problem in a new space, Boundary Value Problems, 2014 (2014), 2014:153.
6	H-C. Pak and Y-J. Park, Spectrum and Singular Integrals on a New Weighted Function Space, Acta Mathematica Sinica, English Series, 34 (2018), no. 11, 1692-1702. DOI