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We introduce the notion of linear multifractional stable sheets in the broadsense (LMSS) with $\alpha\in(0,2]$, to include both linear multifractionalBrownian sheets ($\alpha=2$) and linear multifractional stable sheets($\alpha<2$). The purpose of the present paper is to study the existence andjoint continuity of the local times of LMSS, and also the local H\"oldercondition of the local times in the set variable. Among the main results ofthis paper, Theorem 2.4 provides a sufficient and necessary condition for theexistence of local times of LMSS; Theorem 3.1 shows a sufficient condition forthe joint continuity of local times; and Theorem 4.1 proves a sharp localH\"older condition for the local times in the set variable. All these theoremsimprove significantly the existing results for the local times ofmultifractional Brownian sheets and linear multifractional stable sheets in theliterature.

Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times