See the is no restriction on lease of agriculture land.
For purchase of agriculture land in karnataka the family income should be below 25 lakh under sectio. 79A karnataka land reform Act.
Also the deputy commissioners is required grant permission for non-agriculturists to purchase agricultural land under Section 80 of the Act.
So yes you can. Buy you need your family income proof ID proofs a grant from the deputy commissioners along with other requisites for sale.
For leases no as such document other that ID proof and land documents ia needed.
No company can purchase agriculture land in karnataka
Also for industry there are some similar provision stating if you are forming company for purchase of agricultural land in Karnataka you have to obtain approval of high powered committee for purchase of agricultural land. you would need approval from state govt of Karnataka.