What is claimed is:1. A method of manufacturing a light-emitting device, the method comprising:providing a first intermediate product including:a base member having a recess, anda light-emitting element placed on or above an inner bottom surface of the base member;injecting into the recess a resin including a light-diffusing agent that includes hollow particles to form a light-transmissive member in a convex shape with a thickness that gradually increases from a peripheral portion of the light-transmissive member toward a central portion of the light-transmissive member;allowing the hollow particles to float up to a first surface of the injected light-transmissive member and to gather in the central region of the light-transmissive member; andhardening the light-transmissive member to form the light-emitting device,wherein, in a plan view, the central portion of the first surface of the light-transmissive member has irregularities formed by the light-diffusing agent and a peripheral region including the outer peripheral portion of the first surface of the light-transmissive member is smooth without the irregularities formed by the light-diffusing agent.2. The method of manufacturing a light-emitting device according to claim 1,wherein the light-transmissive member further comprises a phosphor, andwherein, the light-transmissive member is formed so that the phosphor density at the light-emitting element side of the light-transmissive member is higher than the phosphor density at the first surface side of the light-transmissive member.3. The method of manufacturing a light-emitting device according to claim 1, wherein the hollow particles are allowed to float up so that at least a portion of the light-diffusing agent is exposed at the first surface of the light-transmissive member and/or the light-diffusing agent is covered with the light-transmissive member to form irregularities by the hollow particles on the first surface of the light-transmissive member.4. The method of manufacturing a light-emitting device according to claim 1, wherein the light-diffusing agent has a particle size in a range of 20 μm to 70 μm.5. The method of manufacturing a light-emitting device according to claim 1, wherein the light-diffusing agent has a bulk density relative to the light-transmissive member in a range of 0.1 g/cm3 to 0.7 g/cm3.6. The method of manufacturing a light-emitting device according to claim 1, wherein the hollow particles are allowed to float up so that the light-diffusing agent is located at the central region of the light-transmissive member in a plan view and the light-diffusing agent is not present at the peripheral portion of the light-transmissive member in a cross-sectional view.7. The method of manufacturing a light-emitting device according to claim 1, wherein the hollow particles have a spherical shape.8. The method of manufacturing a light-emitting device according to claim 1, wherein the light-emitting device comprises a plurality of the light-emitting elements.9. The method of manufacturing a light-emitting device according to claim 1, wherein a base material of the light-transmissive member comprises a silicone resin.