Global Well-posedness of Generalized Magnetohydrodynamics Equations in Variable Exponent Fourier-Besov-Morrey Spaces

Parametric Marcinkiewicz Integral and Its Higher-Order Commutators on Variable Exponents Morrey-Herz Spaces

“…Case 1. 1 < q < ∞, by the fact that nδ 2 − α + + ððn − 1Þ/sÞ > 0, the Hölder's inequality, and the inequality (36), it follows that…”

“…In the last decades, the variable Lebesgue spaces have been intensively studied since the pioneering work of [32] by Kovácık and Rákosnık. Additionally, different studies on variable function spaces, such as variable exponents Fourier-Besov-Morrey spaces [33][34][35], variable exponents Fourier-Besov spaces [36,37], variable exponent Morrey spaces [38], variable Bessel potential spaces [39,40], and variable exponent Hardy spaces [41,42], were developed due to their applications in the modeling of electrorheological fluids, PDEs with nonstandard growth, and image restoration. Recently, Izuki studied the Herz spaces [43,44].…”