No, you never italicize the name of the author, and you only italicize the title of the work if it is a book. If you are referring to a short story you put the title of the story in quotes. This is what you should do if your essay is about Alice Munro's story "Boys and Girls." (Notice that the period at the end of the sentence comes inside the closing quotation mark.) Titles of poems and essays and other short pieces are also put in quotes. Titles of plays are customarily italicized. You can see in the reference link below how Alice Munro's "Boys and Girls" is set off in quotes.
Morrison, Clarke . "Are Dogwoods Doomed? . " The Asheville Citizen. September 14, 1990. Carolina Mountain Club Archives. D. H. Ramsey Library Special Collections. University of North Carolina at Asheville, Asheville, NC.
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