It probably depends on which part of the Sherman act we are talking about.
Section 2, which covers "Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce [...]" has been found by courts, I believe, to require 50% market share (or sometimes more) to apply.
But section 1, which applies to "Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce [...]", does not as far as I've been able to tell have any market size threshold.
Section 2, which covers "Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce [...]" has been found by courts, I believe, to require 50% market share (or sometimes more) to apply.
But section 1, which applies to "Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce [...]", does not as far as I've been able to tell have any market size threshold.