we provide sharp two-sided estimates on the tail probability of the first hitting time of a bounded interval. Finally, in Subsection \[subsec:ex\] we indicate a wide class of non-symmetric processes which satisfy assumptions of Theorem \[thm:main\_hitting\_time\].

Preliminaries {#sec:prelims}
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[**Notation**]{}. Throughout the paper $c,c_1,C_1,...$ denote positive constants which may vary from line to line during estimates. We write $c=c(a)$ when $c$ depends only on parameter $a$. For two numbers $a$, $b$ we denote $a \wedge b = \min \{a,b\}$. For two functions $f,g$ we write $f \approx g$ if the ratio $f(u)/g(u)$ stays between two positive constants. Similarly, we write $f \lesssim g$ ($f \gtrsim g$) if the ratio is bounded from above (below) by a positive constant. By $f \cong cg$, $x \to x_0$, we mean that $\lim_{x \to x_0} f(x)/g(x)=c$. We write $f(x) = \mathcal{O}(g(x))$, $x \to x_0$, if $\limsup_{x \to x_0} |f(x)|/g(x)<\infty$. For a complex-valued function $f \colon {\mathbb{R}}\mapsto {\mathbb{C}}$, by $f^{-1}$ we denote its generalized inverse, that is $f^{-1}(s) = \sup \{r>0\colon f^*(r)=s\}$, where $f^*(r) = \sup_{|x| {\leqslant}r} {\operatorname{Re}}f(x)$. Borel sets on the real line are denoted by ${\mathcal{B}}_{{\mathbb{R}}}$ .

Throughout the whole paper we let $\mathbf{X}=(X_t\colon t {\geqslant}0)$ be a one-dimensional Lévy process with the 