来週の日曜なら空いてます。

next week

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

Sunday

be; is; indicates past or completed action; indicates light imperative

to open (e.g. doors); to open (e.g. business, etc.); to be empty; to be vacant; to be available; to be free; to be open (e.g. neckline, etc.); to have been opened (of one's eyes, mouth, etc.); to come to an end; to open (one's eyes, mouth, etc.); to have a hole; to form a gap; to have an interval (between events)