A: It is common for immigrants coming from other heritages to standardize the spelling of their names.
In this case: Lars Fredrik Pettersson .... you will want to search indexes for all of the spelling options for his name.
Fredrik: Could be spelled Frederick or even the short form: Fred
Pettersson: Could be spelled several ways: Petterson; Peterson; Pederson; Petersen; etc.
His complete name might have been written as:
Lars F. Peterson
Fred L. Peterson
Genealogists learn through trial and error the various ways that individuals and record keepers might have spelled their names.
Keep this in mind when you search newspapers.