DOI: 10.1155/jofs/2208011 ISSN: 2314-8896

Fourier Multiplier Theorems on Variable Exponent Lebesgue–Bochner Spaces and Applications

Yuchen Zhong
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We establish the Mikhlin‐type Fourier multiplier theorems on variable exponent Lebesgue–Bochner spaces using the Fourier multiplier theorems on weighted Lebesgue–Bochner spaces and the transform results of bounded operators from weighted spaces to variable exponent spaces. Using the multiplier theorems, we discuss the L p (·) ‐well‐posedness of the first‐order and second‐order differential equations.

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