@article{Al-Azri2024, 
author = {Badriya Al-Azri and Ahmad Al-Salman},
title = {Weighted        L          p       norms of Marcinkiewicz functions on product domains along surfaces},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {8386-8405},
keywords = {Marcinkiewicz integral operators on product domains, weighted Lp norm, maximal functions, Hardy Littlewood maximal function, convex functions},
url = {https://www.sciopen.com/article/10.3934/math.2024408},
doi = {10.3934/math.2024408},
abstract = {We prove a weighted        L          p       boundedness of Marcinkiewicz integral operators along surfaces on product domains. For various classes of surfaces, we prove the boundedness of the corresponding operators on the weighted Lebsgue space        L          p        (            R              n        ×            R              m        ,        ω          1        (  x  )  d  x  ,        ω          2        (  y  )  d  y  ), provided that the weights        ω          1       and        ω          2       are certain radial weights and that the kernels are rough in the optimal space    L  (  log  ⁡  L  )  (            S              n      −      1        ×            S              m      −      1        ). In particular, we prove the boundedness of Marcinkiewicz integral operators along surfaces determined by mappings that are more general than polynomials and convex functions. Also, in this paper we prove the weighted        L          p       boundedness of the related square and maximal functions. Our weighted        L          p       inequalities extend as well as generalize previously known        L          p       boundedness results.}
}