FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION –

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Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “The variable Lebesgue spaces have already widely used in the study of harmonic analysis; see, for example, [10, 9, 11, 14, 15, 48, 26].”
Variable weak Hardy spaces and their applications (2016, background): “The study of variable Lebesgue spaces can be traced back to Orlicz [33], however, they have been the subject of more intensive study since the early 1990s because of their intrinsic interest for applications into harmonic analysis, partial differential equations and variational integrals with nonsta”
Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, methodology): “We refer to [15,20,32] and references therein for the recent progress on Lebesgue spaces with variable exponents and some applications in PDEs and variational integrals with nonstandard growth conditions.”
Characterizations of variable exponent Hardy spaces via Riesz transforms (2015, background): “As a generalization of classical Lebesgue spaces, variable exponent Lebesgue spaces were introduced by Orlicz [17] in 1931, however, they have been the subject of more intensive study since the early 1990s, because of their intrinsic interest for applications into harmonic analysis, partial differen”
Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “[33] gave out an elementary introduction to function spaces with variable exponents and a survey of related function spaces.”