Boundedness of an intrinsic square function on grand $ p $-adic Herz-Morrey spaces

Abstract

<abstract><p>This research paper focuses on establishing a framework for grand Herz-Morrey spaces defined over the $ p $-adic numbers and their associated $ p $-adic intrinsic square function. We will define the ideas of grand $ p $-adic Herz-Morrey spaces with variable exponent $ {M\dot{K} ^{\alpha, u), \theta}_{ s(\cdot)}(\mathbb{Q}^n_p)} $ and $ p $-adic intrinsic square function. Moreover, the corresponding operator norms are estimated. Grand $ p $-adic Herz-Morrey spaces with variable exponent is the generalization of $ p $-adic Herz spaces. Our main goal is to obtain the boundedeness of $ p $-adic intrinsic square function in grand $ p $-adic Herz-Morrey spaces with variable exponent $ {M\dot{K} ^{\alpha, u), \theta}_{ s(\cdot)}(\mathbb{Q}^n_p)} $. The boundedness is proven by exploiting the properties of variable exponents in these function spaces.</p></abstract>