In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on Lp(Rd) for each p is an element of (1, infinity). Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which are not necessarily radial. To do so, we make use of modified square function estimates and bilinear interpolation. For the bilinear interpolation we introduce a function space Sigma 2(B) where B denotes a Banach space of functions on Rd, which is a variant of weighted Sobolev spaces. In result, we obtain convergence results for fractional half-wave equations and surface averages as well as the Lp boundedness for the maximal operators.(c) 2023 Elsevier Inc. All rights reserved.
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