JournalsprimsVol. 55, No. 2pp. 259–282

Weak Triebel–Lizorkin Spaces with Variable Integrability, Summability and Smoothness

  • Wenchang Li

    Hainan Normal University, Haikou, China
  • Jingshi Xu

    Hainan Normal University, Haikou, China
Weak Triebel–Lizorkin Spaces with Variable Integrability, Summability and Smoothness cover
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Abstract

Weak Triebel–Lizorkin spaces with variable integrability, summability and smoothness are first introduced. Then we establish a vector estimate for weak Lebesgue spaces with variable exponent. As an application we give equivalent quasi-norms in these new spaces by means of Peetre's maximal functions. Finally, we obtain the boundedness of the φ\varphi transform on these new spaces and their atomic and molecular decompositions.

Cite this article

Wenchang Li, Jingshi Xu, Weak Triebel–Lizorkin Spaces with Variable Integrability, Summability and Smoothness. Publ. Res. Inst. Math. Sci. 55 (2019), no. 2, pp. 259–282

DOI 10.4171/PRIMS/55-2-2