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Let $L$ be a linear operator on $L^2(mathbb R^n)$ generating an analytic semigroup ${e^{-tL}}_{tge0}$ with kernels having pointwise upper bounds and $p(cdot): mathbb R^nto(0,1]$ be a variable exponent function satisfying the globally log-Holder continuous condition. In this article, the authors introduce the variable exponent Hardy space associated with the operator $L$, denoted by $H_L^{p(cdot)}(mathbb R^n)$, and the BMO-type space ${mathrm{BMO}}_{p(cdot),L}(mathbb R^n)$. By means of tent spaces with variable exponents, the authors then establish the molecular characterization of $H_L^{p(cdot)}(mathbb R^n)$ and a duality theorem between such a Hardy space and a BMO-type space. As applications, the authors study the boundedness of the fractional integral on these Hardy spaces and the coincidence between $H_L^{p(cdot)}(mathbb R^n)$ and the variable exponent Hardy spaces $H^{p(cdot)}(mathbb R^n)$.
Let $p(cdot): mathbb R^nto(0,infty)$ be a variable exponent function satisfying that there exists a constant $p_0in(0,p_-)$, where $p_-:=mathop{mathrm {ess,inf}}_{xin mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal operator is bounded on the
Let $p(cdot): mathbb R^nto(0,1]$ be a variable exponent function satisfying the globally $log$-Holder continuous condition and $L$ a non-negative self-adjoint operator on $L^2(mathbb R^n)$ whose heat kernels satisfying the Gaussian upper bound estima
Let $L$ be a one-to-one operator of type $omega$ in $L^2(mathbb{R}^n)$, with $omegain[0,,pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(cdot): mathbb{R}^nto(0,,1]$ be a variable exponent
We obtain some nonlocal characterizations for a class of variable exponent Sobolev spaces arising in nonlinear elasticity theory and in the theory of electrorheological fluids. We also get a singular limit formula extending Nguyen results to the anisotropic case.
Let $p(cdot): mathbb R^nto(0,infty)$ be a variable exponent function satisfying the globally log-Holder continuous condition. In this article, the authors first introduce the variable weak Hardy space on $mathbb R^n$, $W!H^{p(cdot)}(mathbb R^n)$, via