Under which integrability condition is the convolution with a Dirac comb well-defined?

Question

Let $\delta_x$ denote the Dirac meaure at $x$ on $\mathbb R$ and $$\Delta_Tf:=\sum_{k\in\mathbb Z}f(kT)\delta_{kT}$$ for $T>0$ and $f:\mathbb R\to\mathbb C$. If $h:\mathbb R\to\mathbb R$ is Borel measurable, then the convolution $h\ast\Delta_Tf$ is well-defined iff $$\int\left|h(x-y)\right|\left|\Delta_Tf\right|({\rm d}y)<\infty\;\;\;\text{for all }x\in\mathbb R\tag1,$$ where $\left|\Delta_Tf\right|$ denotes the total variation measure of $\Delta_Tf$. Is there a nice expression for $\left|\Delta_Tf\right|$ such that condition $(1)$ can be simplified?

Answer 1

By the definition of the Dirac delta, this is the same as $$ \sum_{k\in\Bbb Z} |h(x-kT)|\,|f(kT)| < \infty. $$ Is this simpler?