# understanding of the rank-2 tensor as an integral kernel

Let $G\subset{\mathbb R}^m$ be a nonempty compact and Jordan measurable set that coincides with the closure of its interior. Let $K:G\times G\to{\mathbb C}$ be a continuous function. Then we can define an linear operator $A:C(G)\to C(G)$ as $$(A\phi)(x):=\int_G K(x,y)\phi(y)dy,\quad x\in G.$$ If the kernel $K$ is defined and continuous for all $x,y\in G\subset{\mathbb R}^m, x\neq y$, and there exist positive constants $M$ and $\alpha\in(0,m]$ such that $$|K(x,y)|\leq M|x-y|^{\alpha-m}, \quad x,y\in G, x\neq y,$$ the kernel $K$ is called weakly singular.

The definitions above are from Linear Integral Equations by Rainer Kress.

Here are my questions:

If the kernel is a rank-2 tensor, for example, the Oseen tensor in this wiki-article about Stokes flow, can I define the concept that "the kernel is weakly singular"? If the answer is YES, how should I do it? One possible way I think is using some norm of matrices.

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