Sharp estimates of the modified Hardy Littlewood maximal operator on the nonhomogeneous space via covering lemmas

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FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “2) for M ′ 3 and M2 we refer to [160] and [201, 217] respectively.”
Morrey Spaces for Non–doubling Measures (2005, unknown): “We also have the inequality of Fefferman-Stein type. Proposition 2.2 ([ 8 ]).”
Generalized Morrey Spaces for Non-doubling Measures (2008, unknown): “: L p (μ) , which is established in [ 12, Theorem 1.7 ].”
Random Martingales and localization of maximal inequalities (2009, background): “(18) The factor 2 in (9) cannot be replaced by any smaller number while still retaining linear behavior in terms of K of the weak (1, 1) operator norm; see [43].”
Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces for nondoubling measures (2009, background): “This theorem is a good contrast to [10].”