TY - JOUR
T1 - Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces
AU - Karlovich, Alexei
N1 - Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matemática e Aplicações).
PY - 2020/8/1
Y1 - 2020/8/1
N2 - We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results are new even in the case of standard Lebesgue spaces and give answers on two questions about algebras of continuous Fourier multipliers on Lebesgue spaces over the real line posed by Mascarenhas, Santos and Seidel.
AB - We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results are new even in the case of standard Lebesgue spaces and give answers on two questions about algebras of continuous Fourier multipliers on Lebesgue spaces over the real line posed by Mascarenhas, Santos and Seidel.
KW - Continuous Fourier multiplier
KW - piecewise continuous function
KW - slowly oscillating function
KW - Stechkin’s inequality
KW - variable Lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=85086587832&partnerID=8YFLogxK
U2 - 10.1007/s00009-020-01537-z
DO - 10.1007/s00009-020-01537-z
M3 - Article
AN - SCOPUS:85086587832
SN - 1660-5446
VL - 17
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 4
M1 - 102
ER -