In this research paper, we give a brief overview of the variable exponent Lebesgue spaces for 1≤ p(x)<∞. We also mention some applications of variable exponent Lebesgue spaces. We then mainly deal with continuous dual space of variable exponent Lebesgue spaces for 0<p(x)<1 It is known that there exists no nonzero continuous linear functional on classical Lebesgue space Lp when 0<p<1 . We generalize this result to the variable exponent setting. We prove that if p⁺ <1, then the only continuous linear functional on Lp⁽˙⁾Ω(0<p(x)<1) is the zero functional. However, it remains an open question whether there exists non zero continuous linear functional when p₊=1.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Research Article |
Authors | |
Publication Date | June 30, 2020 |
Submission Date | October 31, 2019 |
Acceptance Date | January 7, 2020 |
Published in Issue | Year 2020 Volume: 10 Issue: 1 |
This work is licensed under a Creative Commons Attribution 4.0 International License.