具有可变光滑指标的弱 Musielak-Orlicz-Triebel-Lizorkin 空间

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Weak Musicelak-Orlicz-Triebel-Lizorkin Spaces with Variable Smooth Exponent

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Abstract:

Weak Musielak-Orlicz-Triebel-Lizorkin spaces with variable smooth exponent are first introduced. Then we establish a vector estimate for weak Musielak-Orlicz spaces. 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 $\varphi$ transform on these new spaces and their atomic and molecular decompositions.

Key words: variable smooth exponent, weak Musielak-Orlicz space, triebel-Lizorkin space, atom, molecule, maximal function

CLC Number:

O177.1

Yujiao Dai, Jingshi Xu. Weak Musicelak-Orlicz-Triebel-Lizorkin Spaces with Variable Smooth Exponent[J].Acta mathematica scientia,Series A, 2025, 45(3): 687-701.

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