Does the following hold?

For every bipartite graph $H$ and every graph $G$ with $e(G)\geq 0.1(v(G))^2$, $$t(H,G)\geq t(K_2, G)^{e(H)}.$$

If not sure, is this a equal question as Sidorenko's conjecture or a subquestion of Sidorenko?

$t(H,G)$ means: Take a random onto map $f$ from $V(H) \to V(G)$, the prob. that this map keep adjacency, i.e. a~b implies f(a)~f(b). If G's adjacency matrix's every element is 1, then for every $H$, $t(H,G)=V(G)^{V(H)}/V(G)^{V(H)}=1$.