Littlewood-Paley Characterizations of Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces

By Der-Chen Chang, Songbai Wang, Dachun Yang, Yangyang Zhang. Complex Analysis and Operator Theory, 2019

60 citations recorded by the source corpus.

Let X be a ball quasi-Banach function space on $${{\mathbb {R}}}^n$$ R n . In this article, assuming that the powered Hardy–Littlewood maximal operator satisfies some Fefferman–Stein vector-valued maximal inequality on X and is bounded on the associated space, the authors establish various Littlewood–Paley function characterizations of the Hardy space $$H_X({{\mathbb {R}}}^n)$$ H X ( R n ) associated with X , under some weak assumptions on the Littlewood–Paley functions. To this end, the authors also establish a useful estimate on the change of angles in tent spaces associated with X . All these results have wide applications. Particularly, when $$X:=M_r^p({{\mathbb {R}}}^n)$$ X : = M r p ( R n ) (the Morrey space), $$X:=L^{\vec {p}}({{\mathbb {R}}}^n)$$ X : = L p → ( R n ) (the mixed-norm Lebesgue space), $$X:=L^{p(\cdot )}({{\mathbb {R}}}^n)$$ X : = L p ( · ) ( R n ) (the variable Lebesgue space), $$X:=L_\omega ^p({{\mathbb {R}}}^n)$$ X : = L ω p ( R n ) (the weighted Lebesgue space) and $$X:=(E_\Phi ^r)_t({{\mathbb {R}}}^n)$$ X : = ( E Φ r ) t ( R n ) (the Orlicz-slice space), the Littlewood–Paley function characterizations of $$H_X({{\mathbb {R}}}^n)$$ H X ( R n ) obtained in this article improve the existing results via weakening the assumptions on the Littlewood–Paley functions and widening the range of $$\lambda $$ λ in the Littlewood–Paley $$g_\lambda ^*$$ g λ ∗ -function characterization of $$H_X({\mathbb {R}}^n)$$ H X ( R n ) .

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/986c0bdcb9924b634382abd13b36c3bd8d176057

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In Applied Mathematics

  1. Wen Yuan
  2. Dachun Yang
  3. Xianjie Yan
  4. Jun Liu
  5. Yoshihiro Sawano
  6. Ciqiang Zhuo
  7. Yangyang Zhang
  8. Songbai Wang

In Mathematical Physics

  1. Wen Yuan
  2. Dachun Yang
  3. Xianjie Yan
  4. Yoshihiro Sawano
  5. Ciqiang Zhuo
  6. Jun Liu
  7. Yangyang Zhang
  8. Songbai Wang

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