This year Tisha B'Av falls on Shabbat. Is shaving allowed in honor of Shabbat?
From this site:
Many Ashkanazi Jews refrain from haircutting and shaving during the Three Weeks, and even those who are lenient in this regard on Fridays, in honor of the Sabbath, do not cut their hair or shave for Shabbat Chazon. For Sephardi Jews it is permissible to shave and cut hair for Shabbat Chazon. Even if Shabbat Chazon immediately precedes Tisha B’Av, it is permissible, strictly speaking, according to Sephardic custom, to shave or have one’s hair cut for the Sabbath. One who chooses to behave stringently in this regard merits a divine blessing.
My own addition - Regarding Sephardim, their custom of mourning applies only to the week that Tish'a B'av occurs. When Tisha B'av occurs on Sunday or is postponed to Sunday, as it is this year and next (5778 and 5779), there is no such "week".