What is the right exponent such that $f, g\in L^p(\mathbb{R}^3)$?

Question

Consider the functions $f(x)=\frac{1}{x}$ and $g(x)=M$, where $M$ denotes a constant. What are the right exponents $p, q$ such that $f(x)\in H^p(\mathbb{R}^3)$ and $g(x)\in H^q(\mathbb{R}^3)$?

Moreover, there exists an exponent $r$ such that both $f(x), g(x)\in H^r(\mathbb{R}^3)$?

Thank you in advance!