Boundedness of Littlewood-Paley-Stein (LPS) Operator in Lebesgue Space with an Improved Sufficient Condition

Pebrudal Zanu1, Wono Setya Budhi2, Yudi Soeharyadi3
Reaserch Division of Analysis and Geometry, Mathematics and Natural Science Faculty, Institut Teknologi Bandung

1pebrudal@gmail.com, 2wono@math.itb.ac.id, 3yudish@math.itb.ac.id

Abstract

Littlewood-Paley-Stein (LPS) operator is operator that maps a function to square function associated with a function ψ, that is . Littlewood-Paley established a sufficient condition for boundedness of LPS operator in classical Lebesgue Space. The condition is expressed in term of bound for sum |ψ| + |∇ψ|. In this article, we investigate and prove boundednesss of LPS operator with a generalized version for the bound from the original version.

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References

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Cite this paper as:
Zanu P, Budhi W S and Soeharyadi Y 2019 Boundedness of Littlewood-Paley-Stein (LPS) Operator in Lebesgue Space with an Improved Sufficient Condition Proc. Int. Conf. on Mathematical Analysis, Its Applications and Learning (15 September 2018, Yogyakarta) ed B Utomo (Yogyakarta: Sanata Dharma University Press) pp 111–115