TY - JOUR
T1 - INVERTIBILITY OF FOURIER CONVOLUTION OPERATORS WITH PC SYMBOLS ON VARIABLE LEBESGUE SPACES WITH KHVEDELIDZE WEIGHTS
AU - Fernandes, Cláudio
AU - Karlovych, Oleksiy
AU - Medalha, Samuel
N1 - Funding Information:
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/10/10
Y1 - 2022/10/10
N2 - Let p(·) : R→ (1 , ∞) be a sufficiently regular variable exponent and ϱ be a Khvedelidze weight on R. Suppose that a function a belongs to the algebra PCp(·),ϱ of piecewise continuous Fourier multipliers on the weighted variable Lebesgue space Lp(·)(R, ϱ). We show that the Fourier convolution operator W(a) = F- 1aF is invertible on the space Lp(·)(R, ϱ) if and only if its symbol a is invertible in L∞(R).
AB - Let p(·) : R→ (1 , ∞) be a sufficiently regular variable exponent and ϱ be a Khvedelidze weight on R. Suppose that a function a belongs to the algebra PCp(·),ϱ of piecewise continuous Fourier multipliers on the weighted variable Lebesgue space Lp(·)(R, ϱ). We show that the Fourier convolution operator W(a) = F- 1aF is invertible on the space Lp(·)(R, ϱ) if and only if its symbol a is invertible in L∞(R).
KW - Fourier convolution operator
KW - Fourier multiplier
KW - Invertibility
KW - Khvedelidze weight
KW - Piecewise continuous function
KW - Variable Lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=85139719313&partnerID=8YFLogxK
U2 - 10.1007/s10958-022-05897-7
DO - 10.1007/s10958-022-05897-7
M3 - Article
AN - SCOPUS:85139719313
SN - 1072-3374
JO - Journal of Mathematical Sciences (United States)
JF - Journal of Mathematical Sciences (United States)
ER -