Let $(X, d, \mu )$ be a metric measure space endowed with a distance $d$ and a nonnegative Borel doubling measure $\mu $. Let $L$ be a non-negative self-adjoint operator of order $m$ on $L^2(X)$. Assume that the semigroup ${\rm e}^{-tL}$ generated by $L$ satisfies the Davies-Gaffney estimate of order $m$ and $L$ satisfies the Plancherel type estimate. Let $H^p_L(X)$ be the Hardy space associated with $L.$ We show the boundedness of Stein's square function ${\mathcal G}_{\delta }(L)$ arising from Bochner-Riesz means associated to $L$ from Hardy spaces $H^p_L(X)$ to $L^{p}(X)$, and also study the boundedness of Bochner-Riesz means on Hardy spaces $H^p_L(X)$ for $0<p\leq 1$.
The aim of the article is to introduce female characters of Serbian epic poems and Ukrainian dumas in comparative perspective. The focus is laid on the roles and characteristics attributed to women in epic poems relating to the Battle of Kosovo and dumas describing the period of the battles between Cossacks and Turko-Tatar tribes. It is argued that although women in folk literatuře usually have a passive role and their main function is to emphasize the importance of the male sacrifice, there are also examples of active female characters who make their own decisions and thereby influence their own destiny as well as the destiny of others.